An additive problem in the Fourier coefficients of cusp forms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2001
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| Acceso en línea: | |
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| _version_ | 1866912120596070400 |
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| author | Harcos, Gergely |
| author_facet | Harcos, Gergely |
| contents | We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for L-functions associated to character twists of these cusp forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0101096 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | An additive problem in the Fourier coefficients of cusp forms Harcos, Gergely Number Theory Primary 11F30, 11F37, Secondary 11M41 We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for L-functions associated to character twists of these cusp forms. |
| title | An additive problem in the Fourier coefficients of cusp forms |
| topic | Number Theory Primary 11F30, 11F37, Secondary 11M41 |
| url | https://arxiv.org/abs/math/0101096 |