Sharp conditional moment bounds for products of $L$-functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929520699768832 |
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| author | Hagen, Markus Valås |
| author_facet | Hagen, Markus Valås |
| contents | Assuming the Generalized Riemann Hypothesis and the Generalized Ramanujan Conjecture, we determine the order of the $2(k_1,\dots,k_r)$th moment of a product of distinct irreducible $L$-functions on the critical line. As a consequence, we obtain conditional information about the independence of these $L$-functions in the large deviations regime. We also obtain sharp moment bounds for Hurwitz zeta functions with rational parameter, and a certain family of Dedekind zeta functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp conditional moment bounds for products of $L$-functions Hagen, Markus Valås Number Theory Assuming the Generalized Riemann Hypothesis and the Generalized Ramanujan Conjecture, we determine the order of the $2(k_1,\dots,k_r)$th moment of a product of distinct irreducible $L$-functions on the critical line. As a consequence, we obtain conditional information about the independence of these $L$-functions in the large deviations regime. We also obtain sharp moment bounds for Hurwitz zeta functions with rational parameter, and a certain family of Dedekind zeta functions. |
| title | Sharp conditional moment bounds for products of $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.19780 |