On Hecke eigenvalues of Ikeda lifts
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917585697636352 |
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| author | Gun, Sanoli Naik, Sunil L |
| author_facet | Gun, Sanoli Naik, Sunil L |
| contents | A well known result of Breulmann states that Hecke eigenvalues of Saito-Kurokawa lifts are positive. In this article, we show that the Hecke eigenvalues of an Ikeda lift at primes are positive. Further, we derive lower and upper bounds of these Hecke eigenvalues for all primes $p$. One of the main ingredients involves expressing the Hecke eigenvalues of an Ikeda lift in terms of certain reciprocal polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Hecke eigenvalues of Ikeda lifts Gun, Sanoli Naik, Sunil L Number Theory 11F11, 11F30, 11F46, 11N56, 11B65 A well known result of Breulmann states that Hecke eigenvalues of Saito-Kurokawa lifts are positive. In this article, we show that the Hecke eigenvalues of an Ikeda lift at primes are positive. Further, we derive lower and upper bounds of these Hecke eigenvalues for all primes $p$. One of the main ingredients involves expressing the Hecke eigenvalues of an Ikeda lift in terms of certain reciprocal polynomials. |
| title | On Hecke eigenvalues of Ikeda lifts |
| topic | Number Theory 11F11, 11F30, 11F46, 11N56, 11B65 |
| url | https://arxiv.org/abs/2402.06145 |