Paper Citation Record · LEDGER

All modular forms of weight 2 can be expressed by Eisenstein series

As of 16 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:1908.03616.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.03616 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:14:48.829265Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

23 of 23 outbound references displayed

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Outbound references

Observation 6c9239fd-3390-47f3-85c5-dfaf0914fc01 · outbound

This paper cites 4 Eisenstein series In preparation for the proof of this section’ s main theorem, we determine the space of cusp expan- sions of Eisenstein series.

All modular forms of weight 2 can be expressed by Eisenstein series 4 Eisenstein series In preparation for the proof of this section’ s main theorem, we determine the space of cusp expan- sions of Eisenstein series

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.208481Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 977e4849-b021-459d-ba88-abca4498e9cc · outbound

This paper cites Modular forms in Pari/GP.

All modular forms of weight 2 can be expressed by Eisenstein series Modular forms in Pari/GP

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.192804Z

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Observation d3291bc7-5641-4e75-9859-6b5582f779ff · outbound

This paper cites Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves.

All modular forms of weight 2 can be expressed by Eisenstein series Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.177855Z

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Observation 66dc67f2-ea70-4679-af6d-e745ea156441 · outbound

This paper cites A positive proportion of elliptic curves over Q have rank one.

All modular forms of weight 2 can be expressed by Eisenstein series A positive proportion of elliptic curves over Q have rank one

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.162837Z

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Observation 66ec1ed7-9a64-4573-867a-9357e456a319 · outbound

This paper cites Toric modular forms and nonvanishing of L-functions.

All modular forms of weight 2 can be expressed by Eisenstein series Toric modular forms and nonvanishing of L-functions

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.148136Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 708aa310-27f0-48d9-bd8b-18b51a5dcfeb · outbound

This paper cites Toric modular forms of higher weight.

All modular forms of weight 2 can be expressed by Eisenstein series Toric modular forms of higher weight

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.133051Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 41a08edd-a7d5-45e2-9663-a8586248efc2 · outbound

This paper cites Toric varieties and modular forms.

All modular forms of weight 2 can be expressed by Eisenstein series Toric varieties and modular forms

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.118239Z

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Observation 2b24a146-992a-4211-a993-785bb7dba7f8 · outbound

This paper cites On two geometric theta lifts.

All modular forms of weight 2 can be expressed by Eisenstein series On two geometric theta lifts

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.102273Z

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Observation cfb6b88d-be9d-4e85-bb6c-4e711f0b3029 · outbound

This paper cites Generalized moonshine, II: Borcherds products.

All modular forms of weight 2 can be expressed by Eisenstein series Generalized moonshine, II: Borcherds products

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.086700Z

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Observation f82dbdb5-7cb1-4b6d-857d-0a5cefe91d79 · outbound

This paper cites Expansions at cusps and Petersson products in Pari/GP.

All modular forms of weight 2 can be expressed by Eisenstein series Expansions at cusps and Petersson products in Pari/GP

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.071907Z

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Observation 88db78a8-c8a9-42ae-899e-8e68e7637427 · outbound

This paper cites La conjecture de Weil. II.

All modular forms of weight 2 can be expressed by Eisenstein series La conjecture de Weil. II

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.056787Z

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Observation b5fc7675-aa5f-4de3-bfb9-f0fd0308b373 · outbound

This paper cites Products of Eisenstein series and Fourier expansions of modular forms at cusps.

All modular forms of weight 2 can be expressed by Eisenstein series Products of Eisenstein series and Fourier expansions of modular forms at cusps

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.042171Z

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Observation a93cc50f-a94e-4b85-a8ff-f9b28f63bc66 · outbound

This paper cites Nonvanishing theorems for automorphic L-functions on GL(2).

All modular forms of weight 2 can be expressed by Eisenstein series Nonvanishing theorems for automorphic L-functions on GL(2)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.026938Z

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Observation ec829c3f-5515-4c05-bdb2-34e1085c8471 · outbound

This paper cites Conjectures on elliptic curves over quadratic ﬁelds.

All modular forms of weight 2 can be expressed by Eisenstein series Conjectures on elliptic curves over quadratic ﬁelds

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:49.010848Z

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Observation 9b886d49-72ab-437e-8de9-16f750ea465d · outbound

This paper cites Heegner points and derivatives of L-series.

All modular forms of weight 2 can be expressed by Eisenstein series Heegner points and derivatives of L-series

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.995895Z

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Observation f280962c-bb75-4e2f-8526-6ac20e676b55 · outbound

This paper cites Iwaniec and E.

All modular forms of weight 2 can be expressed by Eisenstein series Iwaniec and E

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.980918Z

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Observation 018eb2e0-52e7-47c3-82dd-37b5b45e03fc · outbound

This paper cites Products of two Eisenstein series and spaces of cusp forms of prime level.

All modular forms of weight 2 can be expressed by Eisenstein series Products of two Eisenstein series and spaces of cusp forms of prime level

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.965898Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a1c10b39-3e01-4c96-ac58-4a7efa3ceeba · outbound

This paper cites Modular forms with rational periods.

All modular forms of weight 2 can be expressed by Eisenstein series Modular forms with rational periods

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.949744Z

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Observation 39fa08bf-4f7c-4764-a4d1-1eca6c40daca · outbound

This paper cites an unresolved cited work.

All modular forms of weight 2 can be expressed by Eisenstein series Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:14:48.932300Z

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Observation 8008cbc4-8276-4d7b-8e48-4c41e131296f · outbound

This paper cites Non-vanishing of quadratic twists of modular L-functions.

All modular forms of weight 2 can be expressed by Eisenstein series Non-vanishing of quadratic twists of modular L-functions

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.915876Z

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Observation a47b617f-5852-4380-b7f0-57cf8e34479b · outbound

This paper cites The scalar product of modular forms.

All modular forms of weight 2 can be expressed by Eisenstein series The scalar product of modular forms

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.899439Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 613bf0ea-e972-4864-a3c9-f5cc18cd508f · outbound

This paper cites Sur les coefﬁcients de Fourier des formes modulaires de poids demi-entier.

All modular forms of weight 2 can be expressed by Eisenstein series Sur les coefﬁcients de Fourier des formes modulaires de poids demi-entier

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.883885Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1521ec6c-a455-4189-8e1b-f9ee11d2b52f · outbound

This paper cites Products of vector valued Eisenstein series.

All modular forms of weight 2 can be expressed by Eisenstein series Products of vector valued Eisenstein series

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:14:48.867297Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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