On divisibility of Hecke eigenvalues of Ikeda lifts
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916997298651136 |
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| author | Gun, Sanoli Naik, Sunil |
| author_facet | Gun, Sanoli Naik, Sunil |
| contents | In this article, we estimate the density of the set of primes $p$ such that the $p$-th Hecke eigenvalue of an Ikeda lift is divisible by a fixed positive integer. One of the main ingredients involves the study of abelian subfields of fixed fields of the kernel of Galois representations attached to elliptic Hecke eigenforms. Further, we study the distribution of Fourier coefficients of elliptic Hecke eigenforms in arithmetic progressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On divisibility of Hecke eigenvalues of Ikeda lifts Gun, Sanoli Naik, Sunil Number Theory 11F11, 11F30, 11F46, 11F80, 11N56, 11R45 In this article, we estimate the density of the set of primes $p$ such that the $p$-th Hecke eigenvalue of an Ikeda lift is divisible by a fixed positive integer. One of the main ingredients involves the study of abelian subfields of fixed fields of the kernel of Galois representations attached to elliptic Hecke eigenforms. Further, we study the distribution of Fourier coefficients of elliptic Hecke eigenforms in arithmetic progressions. |
| title | On divisibility of Hecke eigenvalues of Ikeda lifts |
| topic | Number Theory 11F11, 11F30, 11F46, 11F80, 11N56, 11R45 |
| url | https://arxiv.org/abs/2510.07056 |