Divisor problems for restricted Fourier coefficients of modular forms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912984482185216 |
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| author | Lau, Yuk-Kam Lee, Wonwoong |
| author_facet | Lau, Yuk-Kam Lee, Wonwoong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Divisor problems for restricted Fourier coefficients of modular forms Lau, Yuk-Kam Lee, Wonwoong Number Theory 11F30, 11N37 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. |
| title | Divisor problems for restricted Fourier coefficients of modular forms |
| topic | Number Theory 11F30, 11N37 |
| url | https://arxiv.org/abs/2411.17210 |