Breaking the [Formula presented]-barrier for the twisted second moment of Dirichlet L-functions

Hung M. Bui, Kyle Pratt, Nicolas Robles, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

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 [Formula presented]-barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than q51/101=q1/2+1/202. 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.

Original languageEnglish (US)
Article number107175
JournalAdvances in Mathematics
Volume370
DOIs
StatePublished - Aug 26 2020

Keywords

  • Dirichlet L-functions
  • Kloosterman fractions
  • Large sieve inequality
  • Moments
  • Twisted second moment

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Breaking the [Formula presented]-barrier for the twisted second moment of Dirichlet L-functions'. Together they form a unique fingerprint.

Cite this