Primes in arithmetic progressions on average I
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929507341959168 |
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| author | Parry, Tomos |
| author_facet | Parry, Tomos |
| contents | Let $E_x(q,a)$ be the error term when counting primes in arithmetic progressions and let $M(Q)=\sum_{q\leq Q}ϕ(q)\sum_{a=1}^qE_x(q,a)^3$. We show that $M(Q)<<Q^3(x/Q)^{7/5}$ for large $Q$ close to $x$ (in the usual BDH sense) thereby showing that sign changes in the error give power saving cancellation past the expected $\sqrt {x/q}$ heuristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primes in arithmetic progressions on average I Parry, Tomos Number Theory Let $E_x(q,a)$ be the error term when counting primes in arithmetic progressions and let $M(Q)=\sum_{q\leq Q}ϕ(q)\sum_{a=1}^qE_x(q,a)^3$. We show that $M(Q)<<Q^3(x/Q)^{7/5}$ for large $Q$ close to $x$ (in the usual BDH sense) thereby showing that sign changes in the error give power saving cancellation past the expected $\sqrt {x/q}$ heuristic. |
| title | Primes in arithmetic progressions on average I |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.06450 |