Magnetic orthogonal modular forms

Claudia Alfes; Paul Kiefer

REVIEW 2 major objections 4 minor 12 references

Under a vanishing condition, meromorphic orthogonal modular forms are magnetic.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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Kiefer's meromorphic orthogonal modular forms are claimed to be magnetic, but the proof's divisibility exponent falls short for even n>2.

T0 review reviewed 2026-08-02 challenge →

load-bearing objection Useful computation of a Borcherds lift, but the magneticity theorem only goes through for n=2; the even n>2 gap is load-bearing. the 2 major comments →

arxiv 2602.13676 v2 pith:HECL6EQX submitted 2026-02-14 math.NT

Magnetic orthogonal modular forms

Claudia Alfes , Paul Kiefer This is my paper

classification math.NT MSC 11F2711F3011F55

keywords magnetic modular formsorthogonal modular formsWeil representationtheta liftFourier coefficients divisibilityPoincaré seriesharmonic weak Maass formsmeromorphic modular forms

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Meromorphic orthogonal modular forms are called magnetic when their Fourier coefficients satisfy a strong divisibility condition. This paper proves that a family of such forms, defined from sums over lattice vectors of fixed negative norm, is magnetic whenever the space of cusp forms for the associated Weil representation is trivial. The proof proceeds by realizing these meromorphic forms as regularized additive theta lifts of vector-valued weakly holomorphic modular forms, then using the explicit Fourier expansion of the lift to transfer divisibility from the input coefficients to the output coefficients. The result holds for even lattices of signature (2,n) with n even, connecting the arithmetic of Fourier coefficients to the geometry of theta correspondences.

Core claim

Theorem 1.1 asserts that, for an even lattice L of signature (2,n) with n even, the meromorphic orthogonal modular forms ω^{mero}_{β,m}(Z) = Σ_{μ∈β+L, q(μ)=m} (μ, Z + e^{−} − q(Z)e^{1})^{−κ} are magnetic: the Fourier coefficient of index ℓλ_0, where λ_0 is primitive in the closure of the positive cone, is divisible by (Nℓq(λ_0))^{κ−1}, with N the level of L and κ the weight. This holds under the assumption that the space of cusp forms of weight k = 1 − n/2 + κ for the Weil representation ρ_L vanishes. The proof has two stages: first, a calculation shows these ω-functions are constant multiples of the regularized additive theta lift of the vector-valued Poincaré series F_{β,m,k}; second, the

What carries the argument

The regularized additive theta lift Φ_L(f, Z), a linear map from weakly holomorphic modular forms f of weight k for the Weil representation ρ_L to orthogonal modular forms of weight κ = n/2 − 1 + k. Its Fourier expansion (reproduced from a classical theta-lifting theorem) expresses the coefficient at λ as a divisor sum over m | ℓ of m^{n/2 + k − 2} times input coefficients, making divisibility propagate from input to output. The proof also uses the differential operator D^{k−1} (iterated raising operator) to pass between weights 2−k and k, and the fact that Poincaré series provide bases for the relevant spaces of weakly holomorphic modular forms.

Load-bearing premise

The load-bearing premise is that the differentiated and scaled integral basis of weakly holomorphic modular forms has Fourier coefficients divisible by (Nℓ)^{κ−1} for κ = n/2 + k − 1, a stronger divisibility than the (Nℓ)^{k−1} established in Corollary 2.3 for even n > 2.

What would settle it

For an explicit even lattice of signature (2,4) whose Weil-representation cusp-form space is trivial, compute the Fourier coefficient of ω^{mero}_{β,m} at ℓλ_0 for ℓ = 2 and check whether it is divisible by (N·2·q(λ_0))^{κ−1}; a single counterexample would disprove Theorem 1.1.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

If the cusp-form space for the Weil representation is trivial, the ω-functions are magnetic: the coefficient of index ℓλ_0 is divisible by (Nℓq(λ_0))^{κ−1}.
These magnetic orthogonal modular forms satisfy the magneticity-at-every-cusp conjecture discussed in the introduction, as a consequence of the Fourier expansion of the theta lift.
The proof gives a general recipe: any weakly holomorphic modular form with input coefficients divisible by (Nℓ)^{s−1} lifts to a magnetic orthogonal modular form, provided n/2 + k − s − 1 ≥ 0.
For lattices whose discriminant group splits, an extension in the paper produces magnetic forms from invariant vectors and input forms on a smaller lattice.
In signature (2,2), the theorem recovers magnetic Hilbert modular forms, linking the result to known examples of magnetic modular forms.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The gap between the divisibility exponent k−1 supplied by the paper's Corollary 2.3 and the exponent κ−1 required by Theorem 1.1 suggests that, for even n > 2, an additional argument is needed; if such an argument exists, it might remove the need for the trivial-cusp-form assumption.
One could test the theorem numerically for a concrete even lattice of signature (2,4) with trivial cusp-form space, computing the first few Fourier coefficients of ω^{mero}_{β,m} and checking divisibility for ℓ = 2, 3.
The divisor-sum structure in the lift's Fourier expansion hints at multiplicative relations among coefficients that might lead to an Euler-product description of these magnetic forms, though the paper does not explore this.
The connection to Calabi–Yau geometries mentioned in the introduction could be made concrete by checking whether the forms appearing in those physics settings fit into the family considered here.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Useful computation of a Borcherds lift, but the magneticity theorem only goes through for n=2; the even n>2 gap is load-bearing.

read the letter

The paper has one genuinely useful result — Theorem 4.3, computing the additive Borcherds lift of vector-valued Poincaré series as Kiefer's ω^mero — and a clean formal transfer, Corollary 4.2, from Borcherds' Theorem 14.3. That part reads correctly. But Theorem 1.1 as stated is not proven. The proof in Section 5 only supplies input functions whose coefficients are divisible by (Nℓ)^{k−1} (Corollary 2.3), and Corollary 4.2(2) then outputs divisibility (Nℓ q(λ0))^{k−1}. Magneticity requires exponent κ−1 = k−1 + n/2 − 1. For even n > 2 that is strictly larger. No argument in the paper bridges the gap. The N^{k−1} scaling and the constant in Theorem 4.3 rescale the lift; they do not increase ℓ-adic valuation. So the central claim is unsupported for all even n > 2. For n = 2 it reduces to Depouilly's result, which the authors cite.

The reader's stress test is correct, and it is not manufactured. Proposition 2.1 gives integral coefficients, Lemma 2.2 gives the ℓ^{k−1} factor, and nothing controls higher ℓ-adic valuation of the c(γ,ℓ). Corollary 2.3's divisibility is shallow rather than wrong — the coefficients are literally (Nℓ)^{k−1} times integers — but the gap is real.

Should the paper be rejected? The main theorem does not follow, but the paper is not worthless. Theorem 4.3 is a new identity and appears correct; the proof is a standard unfolding computation and the integral evaluation checks out. Corollary 4.2 is a useful packaging of Borcherds' expansion. A serious referee should ask for major revision: either prove the extra divisibility — unlikely from the current arguments — or weaken Theorem 1.1 to the n = 2 case and state the general case as a conjecture. Remark 1.4 overclaims: it suggests a general method, but the same gap applies there.

The citation pattern is fine. The self-citation [17] is appropriate since ω^mero comes from there. The physics references are decorative but not misleading. No invented entities, no free parameters.

Who is this for? People working on Borcherds lifts and the Bönisch–Duhr–Maggio conjectures. The computation will be useful to them even after the main claim is trimmed. I would send it to referees rather than desk-reject: the computation deserves scrutiny and the gap deserves a clear proof or a corrected theorem. Recommendation: major revision, not acceptance.

Referee Report

2 major / 4 minor

Summary. The paper defines a notion of 'magnetic' orthogonal modular forms in signature (2,n) and claims that certain meromorphic orthogonal modular forms \(\omega^{\mathrm{mero}}_{\beta,m}\), recently introduced by Kiefer, are magnetic whenever the space of cusp forms of weight \(k\) for the Weil representation is trivial. The proof strategy is to apply Borcherds' regularized additive theta lift: Section 2 reviews vector-valued modular forms and the Bol operator, Section 3 introduces orthogonal modular forms and the functions \(\omega^{\mathrm{mero}}_{\beta,m}\), Section 4 recalls Borcherds' Fourier expansion and computes the lift of the relevant Poincaré series, and Section 5 attempts to deduce the divisibility claim from Borcherds' theorem. The paper also contains a corollary giving a general divisibility criterion for theta lifts and remarks on connections to physics.

Significance. If Theorem 1.1 were established, it would export the magneticity phenomenon from classical modular forms to higher-dimensional orthogonal groups and would connect to conjectures arising from Feynman-integral calculations. The paper contains some useful ingredients: Theorem 4.3, the explicit lift of vector-valued Poincaré series, appears to be a correct computation, and Corollary 4.2 is a clean formal consequence of Borcherds' Theorem 14.3. However, the central claim of the paper is not proved for the range of dimensions in which it is new. The gap is not a presentation issue; it is an exponent mismatch in the divisibility argument, and it undermines the main theorem as stated.

major comments (2)

[§5, Theorem 1.1] The proof applies Corollary 4.2(2) to the input \(g=N^{k-1}D^{k-1}f\). Corollary 2.3 guarantees only that the Fourier coefficients of \(g\) are divisible by \((N\ell)^{k-1}\), so the only admissible choice in Corollary 4.2(2) is \(s=k\), giving output divisibility \((N\ell q(\lambda_0))^{k-1}\). The magneticity definition in §3.3 requires \((N\ell q(\lambda_0))^{\kappa-1}\) with \(\kappa=n/2+k-1\). For even \(n>2\), \(\kappa-1=k-1+(n/2-1)>k-1\). Lemma 2.2 shows that the Bol operator contributes only \(\ell^{k-1}\), and Proposition 2.1 gives no extra \(\ell\)-adic valuation. Thus Theorem 1.1 is unsupported for every even \(n>2\); for \(n=2\) it reduces to the known case already cited in Remark 1.3.
[§5, Theorem 4.3] Even if the input divisibility were at the required level, the passage from the theta lift to \(\omega^{\mathrm{mero}}_{\beta,m}\) is not automatic. Theorem 4.3 identifies \(\Phi_L(F_{\beta,m,k})\) with \((-2\pi i)^{-\kappa}(\kappa-1)!/(2(k-1)!)\,\omega^{\mathrm{mero}}_{\beta,m}\). Divisibility is not preserved under multiplication by this constant in any obvious way, and the manuscript does not specify the coefficient ring in which the Fourier coefficients are tested for divisibility. The authors need either to define a normalized version of \(\omega^{\mathrm{mero}}_{\beta,m}\) for which the constant is harmless, or to prove that the constant is a unit in the relevant ring; otherwise the conclusion of Theorem 1.1 does not follow from Corollary 4.2.

minor comments (4)

[Abstract] The phrase 'the seminal of work of Borcherds' should read 'the seminal work of Borcherds'.
[§5, last paragraph] The statement 'H_{k,L}=M^!_{k,L}' appears to have an incorrect weight. The Bol operator maps harmonic weak Maass forms of weight \(2-k\) to weakly holomorphic forms of weight \(k\), so the equality should presumably involve \(H_{2-k,L}\), not \(H_{k,L}\). Please correct this notation.
[Corollary 2.3] It would be helpful to state explicitly that the divisibility is an immediate consequence of Lemma 2.2 and the integrality assumption; in particular, Corollary 2.3 does not supply any \(\ell\)-adic valuation beyond the factor \(\ell^{k-1}\). This would clarify why it cannot be used to bridge the gap in Theorem 1.1.
[Theorem 4.1] The phrase 'for sufficiently large |Y|' is used, but the norm \(|Y|\) is not defined. Please specify the norm on \(K\otimes\mathbb R\) used here.

Circularity Check

0 steps flagged

No significant circularity: the magneticity theorem is an application of Borcherds' external theta-lift theorem; the Kiefer self-citation only supplies the definition of the functions being studied.

full rationale

The derivation chain for Theorem 1.1 is: (i) define ω^{mero}_{β,m} following Kiefer [17]; (ii) recall Borcherds' Theorem 14.3, an external result, giving the Fourier expansion of the regularized additive theta lift; (iii) compute in Theorem 4.3 that the lift of the weakly holomorphic Poincaré series F_{β,m,k} is a constant multiple of ω^{mero}_{β,m}; (iv) invoke Corollary 4.2 for divisibility. The only self-citation, Kiefer [17], is load-bearing only as the source of the definition of ω^{mero}; the modularity and cusp-vanishing of these functions are either proved in the paper or follow from the displayed definition, and the divisibility conclusion comes from Borcherds' theorem, not from a property assumed in [17]. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported, and no input is defined in terms of the output. The suspicious step in Section 5 — Corollary 2.3 only gives (Nℓ)^{k−1} while magneticity asks for (Nℓq(λ0))^{κ−1} with κ−1 > k−1 for even n > 2 — is a potential gap in the proof as written, but it is a correctness/verification issue, not circularity: the paper does not define the input divisibility to be the output divisibility, nor does it hide the gap behind a self-citation. Accordingly no circular step is exhibited, and the score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

The central claim rests on Borcherds' external theorem and on the integrality/divisibility of input forms. The only ad hoc element is the unproven identification of the divisibility exponent s with the orthogonal weight κ; this is where the proof fails for n>2.

axioms (6)

standard math Borcherds' Theorem 14.3 gives the Fourier expansion of the regularized additive theta lift.
External foundational theorem [5]; all subsequent divisibility claims depend on it.
standard math Proposition 2.1 (McGraw): M^!_{2−k,L} has a basis with integral Fourier coefficients.
Invoked in Section 5 to supply integral input coefficients; external result [20].
standard math The Bol operator D^{k−1} maps harmonic weak Maass forms of weight 2−k to weakly holomorphic forms of weight k with coefficients scaled by ℓ^{k−1} (Lemma 2.2).
External theorem [9]; the key to Corollary 2.3.
domain assumption The functions ω^{mero}_{β,m} are well-defined meromorphic orthogonal modular forms of weight κ (Kiefer [17]).
The objects under study are adopted from the second author's previous work; the paper cites [17] rather than re-proving well-definedness.
domain assumption The triviality of S_{k,L} implies H_{k,L} = M^!_{k,L}, so the lift's domain is exhausted by holomorphic inputs.
Assumption in Theorem 1.1; used at the end of Section 5 to identify which inputs exist.
ad hoc to paper Implicit assumption that the exponent s in Corollary 4.2 can be taken equal to κ; the proof actually has s = k.
Section 5 invokes Corollary 4.2 for forms whose divisibility is (Nℓ)^{k−1}, i.e. s = k, but the magneticity definition needs s = κ; no argument supplies the missing n/2−1 factors.

reviewed 2026-08-02 · how reviews work

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Cite this review

Pith. "Pith review of Magnetic orthogonal modular forms." pith.science (2026). https://pith.science/paper/HECL6EQX

@misc{pith2026260213676,
  author       = {Pith},
  title        = {Pith review of: Magnetic orthogonal modular forms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HECL6EQX}},
  note         = {Machine review of arXiv:2602.13676}
}

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read the original abstract

In this note we show that certain meromorphic orthogonal modular forms are magnetic, i.e.\ their Fourier coefficients satisfy special divisibility criteria. These meromorphic orthogonal modular forms are counterparts to the orthogonal cusp forms considered by Oda. We show that the seminal of work of Borcherds implies the magneticity of these forms.

discussion (0)

Reference graph

Works this paper leans on

12 extracted references · 4 linked inside Pith

[1]

[2]Bateman, H.Tables of integral transforms [volumes I & II], vol

[1]Ausserlechner, U.A method to compute the hall-geometry factor at weak magnetic field in closed analytical form.Electrical Engineering 98, 3 (2016), 189–206. [2]Bateman, H.Tables of integral transforms [volumes I & II], vol

2016
[6]

[11]Depouilly, B.On the Divisibility Properties of the Fourier Coefficients of Meromorphic Hilbert Modular Forms, arXiv:2411.00701,

Pith/arXiv arXiv
[7]

[12]NIST Digital Library of Mathematical Functions.https://dlmf.nist.gov/, Release 1.2.3 of 2024- 12-15. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, eds. [13]Duhr, C., Maggio, S., Nega, C., Sauer, B., Tancredi, L., and W agner, F. J.Aspects of...

Pith/arXiv arXiv 2024
[9]

[18]Li, Y., and Neururer, M.A magnetic modular form.Int. J. Number Theory 15, 5 (2019), 907–924. [19]L ¨obrich, S., and Schwagenscheidt, M.Arithmetic properties of Fourier coefficients of meromor- phic modular forms.Algebra Number Theory 15, 9 (2021), 2381–2401. [20]McGraw, W. J.The rationality of vector valued modular forms associated with the Weil repre...

2019
[27]

Email address:Paul.Kiefer@uantwerpen.be

MAGNETIC ORTHOGONAL MODULAR FORMS 13 Universit¨at Bielefeld, F akult¨at f ¨ur Mathematik, Postfach 100 131, 33501 Bielefeld, Germany Email address:alfes@math.uni-bielefeld.de Department of Mathematics, University of Antwerp, BE-2000 Antwerp, Belgium. Email address:Paul.Kiefer@uantwerpen.be

2000
[28]

[25]Zagier, D.Modular forms associated to real quadratic fields.Invent. Math. 30, 1 (1975), 1–46. [26]Zemel, S.Integral bases and invariant vectors for Weil representations.Res. Number Theory 9, 1 (2023), Paper No. 5,

1975
[38]

[22]Oda, T.On modular forms associated with indefinite quadratic forms of signaturep2, n´2q.Math. Ann. 231, 2 (1977/78), 97–144. [23]Pa¸sol, V. t., and Zudilin, W.Magnetic (quasi-)modular forms.Nagoya Math. J. 248(2022), 849–864. [24]P ¨ogel, S., W ang, X., and Weinzierl, S.The three-loop equal-mass banana integral inε-factorised form with meromorphic mod...

1977
[1954]

Number Theory 250(2023), 155–182

[3]Bieker, P.Invariants for the Weil representation and modular units for orthogonal groups of signa- ture (2,2).J. Number Theory 250(2023), 155–182. [4]Bieker, P., and Kiefer, P.A converse theorem for borcherds products in signaturep2,2q,

2023
[2002]

H., Ono, K., and Rhoades, R

[9]Bruinier, J. H., Ono, K., and Rhoades, R. C.Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues.Math. Ann. 342, 3 (2008), 673–693. [10]B ¨onisch, K., Duhr, C., and Maggio, S.Some conjectures around magnetic modular forms, arXiv:2404.04085,

Pith/arXiv arXiv 2008
[2017]

[7]Broadhurst, D., and Zudilin, W.A magnetic double integral.J. Aust. Math. Soc. 107, 1 (2019), 9–25. [8]Bruinier, J. H.Borcherds products on O(2,l) and Chern classes of Heegner divisors, vol. 1780 of Lecture Notes in Mathematics. Springer-Verlag, Berlin,

2019
[2024]

E.Automorphic forms with singularities on Grassmannians.Invent

12 CLAUDIA ALFES AND PAUL KIEFER [5]Borcherds, R. E.Automorphic forms with singularities on Grassmannians.Invent. Math. 132, 3 (1998), 491–562. [6]Bringmann, K., Folsom, A., Ono, K., and Rolen, L.Harmonic Maass forms and mock modular forms: theory and applications, vol. 64 ofAmerican Mathematical Society Colloquium Publications. American Mathematical Soci...

1998
[2025]

[14]Duke, W., and Jenkins, P.On the zeros and coefficients of certain weakly holomorphic modular forms.Pure Appl. Math. Q. 4, 4 (2008), 1327–1340. [15]Gross, B., Kohnen, W., and Zagier, D.Heegner points and derivatives ofL-series. II.Math. Ann. 278, 1-4 (1987), 497–562. [16]Jeon, D., Kang, S.-Y., and Kim, C. H.Weak Maass-Poincar´ e series and weight 3/2 m...

Pith/arXiv arXiv 2008

This paper was first reviewed by deepseek-v4-flash on August 2, 2026.

[1] [1]

[2]Bateman, H.Tables of integral transforms [volumes I & II], vol

[1]Ausserlechner, U.A method to compute the hall-geometry factor at weak magnetic field in closed analytical form.Electrical Engineering 98, 3 (2016), 189–206. [2]Bateman, H.Tables of integral transforms [volumes I & II], vol

2016

[2] [6]

[11]Depouilly, B.On the Divisibility Properties of the Fourier Coefficients of Meromorphic Hilbert Modular Forms, arXiv:2411.00701,

Pith/arXiv arXiv

[3] [7]

[12]NIST Digital Library of Mathematical Functions.https://dlmf.nist.gov/, Release 1.2.3 of 2024- 12-15. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, eds. [13]Duhr, C., Maggio, S., Nega, C., Sauer, B., Tancredi, L., and W agner, F. J.Aspects of...

Pith/arXiv arXiv 2024

[4] [9]

[18]Li, Y., and Neururer, M.A magnetic modular form.Int. J. Number Theory 15, 5 (2019), 907–924. [19]L ¨obrich, S., and Schwagenscheidt, M.Arithmetic properties of Fourier coefficients of meromor- phic modular forms.Algebra Number Theory 15, 9 (2021), 2381–2401. [20]McGraw, W. J.The rationality of vector valued modular forms associated with the Weil repre...

2019

[5] [27]

Email address:Paul.Kiefer@uantwerpen.be

MAGNETIC ORTHOGONAL MODULAR FORMS 13 Universit¨at Bielefeld, F akult¨at f ¨ur Mathematik, Postfach 100 131, 33501 Bielefeld, Germany Email address:alfes@math.uni-bielefeld.de Department of Mathematics, University of Antwerp, BE-2000 Antwerp, Belgium. Email address:Paul.Kiefer@uantwerpen.be

2000

[6] [28]

[25]Zagier, D.Modular forms associated to real quadratic fields.Invent. Math. 30, 1 (1975), 1–46. [26]Zemel, S.Integral bases and invariant vectors for Weil representations.Res. Number Theory 9, 1 (2023), Paper No. 5,

1975

[7] [38]

[22]Oda, T.On modular forms associated with indefinite quadratic forms of signaturep2, n´2q.Math. Ann. 231, 2 (1977/78), 97–144. [23]Pa¸sol, V. t., and Zudilin, W.Magnetic (quasi-)modular forms.Nagoya Math. J. 248(2022), 849–864. [24]P ¨ogel, S., W ang, X., and Weinzierl, S.The three-loop equal-mass banana integral inε-factorised form with meromorphic mod...

1977

[8] [1954]

Number Theory 250(2023), 155–182

[3]Bieker, P.Invariants for the Weil representation and modular units for orthogonal groups of signa- ture (2,2).J. Number Theory 250(2023), 155–182. [4]Bieker, P., and Kiefer, P.A converse theorem for borcherds products in signaturep2,2q,

2023

[9] [2002]

H., Ono, K., and Rhoades, R

[9]Bruinier, J. H., Ono, K., and Rhoades, R. C.Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues.Math. Ann. 342, 3 (2008), 673–693. [10]B ¨onisch, K., Duhr, C., and Maggio, S.Some conjectures around magnetic modular forms, arXiv:2404.04085,

Pith/arXiv arXiv 2008

[10] [2017]

[7]Broadhurst, D., and Zudilin, W.A magnetic double integral.J. Aust. Math. Soc. 107, 1 (2019), 9–25. [8]Bruinier, J. H.Borcherds products on O(2,l) and Chern classes of Heegner divisors, vol. 1780 of Lecture Notes in Mathematics. Springer-Verlag, Berlin,

2019

[11] [2024]

E.Automorphic forms with singularities on Grassmannians.Invent

12 CLAUDIA ALFES AND PAUL KIEFER [5]Borcherds, R. E.Automorphic forms with singularities on Grassmannians.Invent. Math. 132, 3 (1998), 491–562. [6]Bringmann, K., Folsom, A., Ono, K., and Rolen, L.Harmonic Maass forms and mock modular forms: theory and applications, vol. 64 ofAmerican Mathematical Society Colloquium Publications. American Mathematical Soci...

1998

[12] [2025]

[14]Duke, W., and Jenkins, P.On the zeros and coefficients of certain weakly holomorphic modular forms.Pure Appl. Math. Q. 4, 4 (2008), 1327–1340. [15]Gross, B., Kohnen, W., and Zagier, D.Heegner points and derivatives ofL-series. II.Math. Ann. 278, 1-4 (1987), 497–562. [16]Jeon, D., Kang, S.-Y., and Kim, C. H.Weak Maass-Poincar´ e series and weight 3/2 m...

Pith/arXiv arXiv 2008

Magnetic orthogonal modular forms

The reading

Core claim §

What carries the argument

Load-bearing premise §

What would settle it §

If this is right

Where Pith is reading between the lines

discussion (0)

Core claim

Load-bearing premise

What would settle it