Divisor problems for restricted Fourier coefficients of modular forms

Yuk-Kam Lau; Wonwoong Lee

Divisor problems for restricted Fourier coefficients of modular forms

Number Theory 2026-03-30 v2

Authors: Yuk-Kam Lau , Wonwoong Lee

Abstract

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.

Keywords

prime number theory modular forms divisor function

Cite

@article{arxiv.2411.17210,
  title  = {Divisor problems for restricted Fourier coefficients of modular forms},
  author = {Yuk-Kam Lau and Wonwoong Lee},
  journal= {arXiv preprint arXiv:2411.17210},
  year   = {2026}
}

Comments

27 pages, accepted by Science China Mathematics

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