A round of Pintz to celebrate oscillations in sums
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910016070483968 |
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| author | Johnston, Daniel R. Trudgian, Tim |
| author_facet | Johnston, Daniel R. Trudgian, Tim |
| contents | We explore a method, going back to Landau and developed by Pintz, for connecting sums of arithmetic functions with zero-free regions for $L$-functions. In particular, we make explicit a general result of Pintz of this form; showing how one can use arithmetical information to deduce information about zeroes of $L$-functions, rather than the other way around. As a prototype, we work through an example with the Riemann zeta-function and sums of the Möbius function, but we also outline the utility of this method in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A round of Pintz to celebrate oscillations in sums Johnston, Daniel R. Trudgian, Tim Number Theory 11M26, 11N56 (Primary) 11M06, 11M41 (Secondary) We explore a method, going back to Landau and developed by Pintz, for connecting sums of arithmetic functions with zero-free regions for $L$-functions. In particular, we make explicit a general result of Pintz of this form; showing how one can use arithmetical information to deduce information about zeroes of $L$-functions, rather than the other way around. As a prototype, we work through an example with the Riemann zeta-function and sums of the Möbius function, but we also outline the utility of this method in general. |
| title | A round of Pintz to celebrate oscillations in sums |
| topic | Number Theory 11M26, 11N56 (Primary) 11M06, 11M41 (Secondary) |
| url | https://arxiv.org/abs/2511.09978 |