Journal
ADVANCES IN MATHEMATICS
Volume 370, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2020.107175
Keywords
Dirichlet L-functions; Twisted second moment; Moments; Kloosterman fractions; Large sieve inequality
Categories
Funding
- NSF [DMS-1501982]
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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 1/2-barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than q(51/101) = q(1/2+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. (C) 2020 Elsevier Inc. All rights reserved.
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