Three conjectures about character sums
| Autor: | Granville, Andrew, Mangerel, Alexander P. |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We establish that three well-known and rather different looking conjectures about Dirichlet characters and their (weighted) sums, (concerning the P\'{o}lya-Vinogradov theorem for maximal character sums, the maximal admissible range in Burgess' estimate for short character sums, and upper bounds for $L(1,\chi)$ and $L(1+it,\chi)$) are more-or-less "equivalent". We also obtain a new mean value theorem for logarithmically weighted sums of 1-bounded multiplicative functions. Comment: 29 pages |
| Databáze: | arXiv |
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