Twisted Kronecker series and periods of modular forms on $Γ_0(N)$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916198338265088 |
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| author | Blakestad, Clifford Choie, YoungJu |
| author_facet | Blakestad, Clifford Choie, YoungJu |
| contents | We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on $Γ_0(N) $ multiplied by their twisted period polynomials in terms of the product of those twisted Kronecker series, when N is square free. This extends an identity of Zagier among period polynomials, Hecke eigenforms and a quotient of Jacobi theta series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Kronecker series and periods of modular forms on $Γ_0(N)$ Blakestad, Clifford Choie, YoungJu Number Theory 11F12, 11F25, 11F50, 11F67 We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on $Γ_0(N) $ multiplied by their twisted period polynomials in terms of the product of those twisted Kronecker series, when N is square free. This extends an identity of Zagier among period polynomials, Hecke eigenforms and a quotient of Jacobi theta series. |
| title | Twisted Kronecker series and periods of modular forms on $Γ_0(N)$ |
| topic | Number Theory 11F12, 11F25, 11F50, 11F67 |
| url | https://arxiv.org/abs/2404.06016 |