Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions
We study the second moment of Dirichlet L-functions to a large prime modulus q twisted by the square of an arbitrary Dirichlet polynomial. We break the -barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than . As an application, we...
| Hoofdauteurs: | , , , |
|---|---|
| Formaat: | Journal article |
| Taal: | English |
| Gepubliceerd in: |
Elsevier
2020
|
| _version_ | 1826285397881126912 |
|---|---|
| author | Bui, HM Pratt, K Robles, N Zaharescu, A |
| author_facet | Bui, HM Pratt, K Robles, N Zaharescu, A |
| author_sort | Bui, HM |
| collection | OXFORD |
| description | We study the second moment of Dirichlet L-functions to a large prime modulus q twisted by the square of an arbitrary Dirichlet polynomial. We break the -barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than . As an application, we obtain an upper bound of the correct order of magnitude for the third moment of Dirichlet L-functions. We give further results when the coefficients of the Dirichlet polynomial are more specialized. |
| first_indexed | 2024-03-07T01:28:13Z |
| format | Journal article |
| id | oxford-uuid:92b22e40-2145-422c-8e60-7539676f7335 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:28:13Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:92b22e40-2145-422c-8e60-7539676f73352022-03-26T23:27:22ZBreaking the 1/2-barrier for the twisted second moment of Dirichlet L-functionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:92b22e40-2145-422c-8e60-7539676f7335EnglishSymplectic ElementsElsevier2020Bui, HMPratt, KRobles, NZaharescu, AWe study the second moment of Dirichlet L-functions to a large prime modulus q twisted by the square of an arbitrary Dirichlet polynomial. We break the -barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than . As an application, we obtain an upper bound of the correct order of magnitude for the third moment of Dirichlet L-functions. We give further results when the coefficients of the Dirichlet polynomial are more specialized. |
| spellingShingle | Bui, HM Pratt, K Robles, N Zaharescu, A Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions |
| title | Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions |
| title_full | Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions |
| title_fullStr | Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions |
| title_full_unstemmed | Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions |
| title_short | Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions |
| title_sort | breaking the 1 2 barrier for the twisted second moment of dirichlet l functions |
| work_keys_str_mv | AT buihm breakingthe12barrierforthetwistedsecondmomentofdirichletlfunctions AT prattk breakingthe12barrierforthetwistedsecondmomentofdirichletlfunctions AT roblesn breakingthe12barrierforthetwistedsecondmomentofdirichletlfunctions AT zaharescua breakingthe12barrierforthetwistedsecondmomentofdirichletlfunctions |