On Fourier coefficients of elliptic modular forms $$\bmod \, \ell $$ with applications to Siegel modular forms
نویسندگان
چکیده
منابع مشابه
Fourier Coefficients of Modular Forms
These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.
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Let d(n) denote the number of divisors of n. In this paper, we study the average value of d(a(p)), where p is a prime and a(p) is the p-th Fourier coefficient of a normalized Hecke eigenform of weight k ≥ 2 for Γ0(N) having rational integer Fourier coefficients.
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In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2021
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-021-01277-8