Pair Correlation of zeros of Dirichlet $L$-Functions: A path towards the Montgomery and Elliott-Halberstam Conjectures
| Autor: | Kandhil, Neelam, Languasco, Alessandro, Moree, Pieter |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet $L$-functions, we establish the truth of a conjecture of Montgomery (in its corrected form stated by Friedlander and Granville) on the magnitude of the error term in the prime number theorem in arithmetic progressions. As a consequence, we obtain that, under the same assumptions, the Elliott-Halberstam conjecture holds true. Comment: 16 pages |
| Databáze: | arXiv |
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