Norm bounds on Eisenstein series
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915248015933440 |
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| author | Kelmer, Dubi Kontorovich, Alex Lutsko, Christopher |
| author_facet | Kelmer, Dubi Kontorovich, Alex Lutsko, Christopher |
| contents | We study the sup-norm and mean-square-norm problems for Eisenstein series on certain arithmetic hyperbolic orbifolds, producing sharp exponents for the modular surface and Picard 3-fold. The methods involve bounds for Epstein zeta functions, and counting restricted values of indefinite quadratic forms at integer points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15162 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Norm bounds on Eisenstein series Kelmer, Dubi Kontorovich, Alex Lutsko, Christopher Number Theory 11M36, 11E45 We study the sup-norm and mean-square-norm problems for Eisenstein series on certain arithmetic hyperbolic orbifolds, producing sharp exponents for the modular surface and Picard 3-fold. The methods involve bounds for Epstein zeta functions, and counting restricted values of indefinite quadratic forms at integer points. |
| title | Norm bounds on Eisenstein series |
| topic | Number Theory 11M36, 11E45 |
| url | https://arxiv.org/abs/2305.15162 |