First Moment of Quadratic Hecke $L$-Functions with Lower Order Term
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914425727877120 |
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| author | Gao, Peng Zhao, Liangyi |
| author_facet | Gao, Peng Zhao, Liangyi |
| contents | We evaluate the first moment of the family of primitive quadratic Hecke $L$-functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First Moment of Quadratic Hecke $L$-Functions with Lower Order Term Gao, Peng Zhao, Liangyi Number Theory 11M06, 11M41 We evaluate the first moment of the family of primitive quadratic Hecke $L$-functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term. |
| title | First Moment of Quadratic Hecke $L$-Functions with Lower Order Term |
| topic | Number Theory 11M06, 11M41 |
| url | https://arxiv.org/abs/2512.22509 |