Pith Number

pith:Y7OJCB5S

pith:2026:Y7OJCB5SURF7X2B6KKHWM6NFWZ

not attested not anchored not stored refs resolved

One-level densities of large even and odd orthogonal families of automorphic L-functions

Micah B. Milinovich, Vorrapan Chandee, Xiannan Li

Conditional on GRH, one-level densities for even and odd orthogonal families of L-functions hold with Fourier support up to 3.

arxiv:2605.17012 v1 · 2026-05-16 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y7OJCB5SURF7X2B6KKHWM6NFWZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove one-level density results for L-functions attached to primitive forms of level q, averaged over square-free q, conditional on the Generalized Riemann Hypothesis (GRH). We treat the even and odd orthogonal families separately and extend the support of the Fourier transform of the test function to (-3,3). This extended support yields the strongest known non-vanishing results for these families of L-functions and their derivatives at the central point, conditional on GRH.

C2weakest assumption

The one-level density statements and the resulting non-vanishing conclusions are conditional on the Generalized Riemann Hypothesis holding for the L-functions in the families under consideration.

C3one line summary

Under GRH, one-level densities for even and odd orthogonal families of automorphic L-functions are established with Fourier support extended to (-3,3), giving the strongest conditional non-vanishing results at the central point.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] S. Baluyot, V. Chandee and X. Li,Low-lying zeros of a large orthogonal family of automorphic L-functions, available on arXiv: https://arxiv.org/abs/2310.07606

[2] O. Barrett, P. Burkhardt, J. DeWitt, R. Dorward, and S.J. Miller,One-level density for holo- morphic cusp forms of arbitrary level.Res. Number Theory, 3: Art. 25, 21,2017 2017

[3] V. Blomer and D. Mili´ cevi´ c.The second moment of twisted modular L-functions. Geom. Funct. Anal., 25(2) (2015), 453 - 516 2015

[4] E. Carneiro, V. Chandee, F. Littmann and M. Milinovich,Hilbert spaces and the pair correlation of zeros of the Riemann zeta function, J. Reine Angrew. Math. (2017) 729, 51-79 2017

[5] E. Carneiro, A. Chirre, and M. B. Milinovich,Hilbert spaces and low-lying zeros of L-functions, Adv. Math. 410 (2022), part B, Paper No. 108748, 48 pp 2022

Receipt and verification

First computed	2026-05-20T00:03:35.876870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7dc9107b2a44bfbe83e528f6679a5b676147f2b6b2b53a97c82c77a70f83c59

Aliases

arxiv: 2605.17012 · arxiv_version: 2605.17012v1 · doi: 10.48550/arxiv.2605.17012 · pith_short_12: Y7OJCB5SURF7 · pith_short_16: Y7OJCB5SURF7X2B6 · pith_short_8: Y7OJCB5S

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Y7OJCB5SURF7X2B6KKHWM6NFWZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c7dc9107b2a44bfbe83e528f6679a5b676147f2b6b2b53a97c82c77a70f83c59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc4fb39ac80932aa84ac8d14a0da6b2ab9182d4c4e5913ccc0e09f823f07f1df",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-16T14:22:24Z",
    "title_canon_sha256": "cb7d2c01a0a39c98a8e496576add71f567a3dc2c37d93c0c453bbecb7729535b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17012",
    "kind": "arxiv",
    "version": 1
  }
}