TY - JOUR
T1 - Breaking the [Formula presented]-barrier for the twisted second moment of Dirichlet L-functions
AU - Bui, Hung M.
AU - Pratt, Kyle
AU - Robles, Nicolas
AU - Zaharescu, Alexandru
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/8/26
Y1 - 2020/8/26
N2 - 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.
AB - 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.
KW - Dirichlet L-functions
KW - Kloosterman fractions
KW - Large sieve inequality
KW - Moments
KW - Twisted second moment
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U2 - 10.1016/j.aim.2020.107175
DO - 10.1016/j.aim.2020.107175
M3 - Article
AN - SCOPUS:85084524665
SN - 0001-8708
VL - 370
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 107175
ER -