Vanishing Fourier coefficients of Hecke eigenforms

Frank Calegari; Naser Talebizadeh Sardari

doi:10.1007/s00208-021-02178-7

Vanishing Fourier coefficients of Hecke eigenforms

Frank Calegari, Naser Talebizadeh Sardari

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove that, for fixed level (N, p) = 1 and p> 2 , there are only finitely many Hecke eigenforms f of level Γ ₁(N) and even weight with a_p(f) = 0 which are not CM.

Original language	English (US)
Pages (from-to)	1197-1215
Number of pages	19
Journal	Mathematische Annalen
Volume	381
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02178-7
State	Published - Dec 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-021-02178-7

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title = "Vanishing Fourier coefficients of Hecke eigenforms",

abstract = "We prove that, for fixed level (N, p) = 1 and p> 2 , there are only finitely many Hecke eigenforms f of level Γ 1(N) and even weight with ap(f) = 0 which are not CM.",

author = "Frank Calegari and {Talebizadeh Sardari}, Naser",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

month = dec,

doi = "10.1007/s00208-021-02178-7",

language = "English (US)",

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AU - Calegari, Frank

AU - Talebizadeh Sardari, Naser

PY - 2021/12

Y1 - 2021/12

N2 - We prove that, for fixed level (N, p) = 1 and p> 2 , there are only finitely many Hecke eigenforms f of level Γ 1(N) and even weight with ap(f) = 0 which are not CM.

AB - We prove that, for fixed level (N, p) = 1 and p> 2 , there are only finitely many Hecke eigenforms f of level Γ 1(N) and even weight with ap(f) = 0 which are not CM.

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U2 - 10.1007/s00208-021-02178-7

DO - 10.1007/s00208-021-02178-7

M3 - Article

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EP - 1215

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3-4

ER -

Vanishing Fourier coefficients of Hecke eigenforms

Abstract

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