The sixth moment of Dirichlet L-functions at the central point
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929483596955648 |
|---|---|
| author | Chandee, Vorrapan Li, Xiannan Matomäki, Kaisa Radziwiłł, Maksym |
| author_facet | Chandee, Vorrapan Li, Xiannan Matomäki, Kaisa Radziwiłł, Maksym |
| contents | In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$-functions at the central point, averaged over primitive characters $χ$ modulo $q$ and all moduli $q \leq Q$. In 2007, as an application of their ``asymptotic large sieve'', Conrey, Iwaniec and Soundararajan showed that when an additional short $t$-averaging is introduced into the problem, an asymptotic can be obtained. In this paper we show that this extraneous averaging can be removed, and we thus obtain an asymptotic for the original moment problem considered by Huxley.
The main new difficulty in our work is the appearance of certain challenging ``unbalanced'' sums that arise as soon as the $t$-aspect averaging is removed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sixth moment of Dirichlet L-functions at the central point Chandee, Vorrapan Li, Xiannan Matomäki, Kaisa Radziwiłł, Maksym Number Theory Primary: 11M06, Secondary: 11M26 In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$-functions at the central point, averaged over primitive characters $χ$ modulo $q$ and all moduli $q \leq Q$. In 2007, as an application of their ``asymptotic large sieve'', Conrey, Iwaniec and Soundararajan showed that when an additional short $t$-averaging is introduced into the problem, an asymptotic can be obtained. In this paper we show that this extraneous averaging can be removed, and we thus obtain an asymptotic for the original moment problem considered by Huxley. The main new difficulty in our work is the appearance of certain challenging ``unbalanced'' sums that arise as soon as the $t$-aspect averaging is removed. |
| title | The sixth moment of Dirichlet L-functions at the central point |
| topic | Number Theory Primary: 11M06, Secondary: 11M26 |
| url | https://arxiv.org/abs/2409.01457 |