Divisor problems for restricted Fourier coefficients of modular forms

Let $d(n)$ be the number of divisors of $n$. We investigate the average value of $d(a_f(p))^r$ for $r$ a positive integer and $a_f(p)$ the $p$-th Fourier coefficient of a cuspidal eigenform $f$ having integral Fourier coefficients, where $p$ is a prime subject to a constraint on the angle associated...

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Bibliographic Details
Main Authors Lau, Yuk-Kam, Lee, Wonwoong
Format Journal Article
LanguageEnglish
Published 26.11.2024
Subjects
Mathematics - Number Theory
Online AccessGet full text
DOI10.48550/arxiv.2411.17210

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Summary:Let $d(n)$ be the number of divisors of $n$. We investigate the average value of $d(a_f(p))^r$ for $r$ a positive integer and $a_f(p)$ the $p$-th Fourier coefficient of a cuspidal eigenform $f$ having integral Fourier coefficients, where $p$ is a prime subject to a constraint on the angle associated with the normalized Fourier coefficient.
DOI:10.48550/arxiv.2411.17210