Murmurations of modular forms in the weight aspect
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908837853790208 |
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| author | Bober, Jonathan Booker, Andrew R. Lee, Min Lowry-Duda, David |
| author_facet | Bober, Jonathan Booker, Andrew R. Lee, Min Lowry-Duda, David |
| contents | We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07746 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Murmurations of modular forms in the weight aspect Bober, Jonathan Booker, Andrew R. Lee, Min Lowry-Duda, David Number Theory 11F30 (Primary), 11N64 (Secondary) We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family. |
| title | Murmurations of modular forms in the weight aspect |
| topic | Number Theory 11F30 (Primary), 11N64 (Secondary) |
| url | https://arxiv.org/abs/2310.07746 |