New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach
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| Format: | Preprint |
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2025
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| _version_ | 1866915126261579776 |
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| author | Tao, Terence Trudgian, Tim Yang, Andrew |
| author_facet | Tao, Terence Trudgian, Tim Yang, Andrew |
| contents | We obtain several new bounds on exponents of interest in analytic number theory, including four new exponent pairs, new zero density estimates for the Riemann zeta-function, and new estimates for the additive energy of zeroes of the Riemann zeta-function. These results were obtained by creating the Analytic Number Theory Exponent Database (ANTEDB) to collect results and relationships between these exponents, and then systematically optimising these relationships to obtain the new bounds. We welcome further contributions to the database, which aims to allow easy conversion of new bounds on these exponents into optimised bounds on other related exponents of interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Tao, Terence Trudgian, Tim Yang, Andrew Number Theory 11L07, 11M06, 11T23 We obtain several new bounds on exponents of interest in analytic number theory, including four new exponent pairs, new zero density estimates for the Riemann zeta-function, and new estimates for the additive energy of zeroes of the Riemann zeta-function. These results were obtained by creating the Analytic Number Theory Exponent Database (ANTEDB) to collect results and relationships between these exponents, and then systematically optimising these relationships to obtain the new bounds. We welcome further contributions to the database, which aims to allow easy conversion of new bounds on these exponents into optimised bounds on other related exponents of interest. |
| title | New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach |
| topic | Number Theory 11L07, 11M06, 11T23 |
| url | https://arxiv.org/abs/2501.16779 |