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TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS

  • LOUBOUTIN, STEPHANE R. (Aix Marseille Universite)
  • Received : 2014.11.21
  • Published : 2015.11.30

Abstract

Given c, a positive integer, we set. $$M(f,c):=\frac{2}{{\phi}(f)}\sum_{{\chi}{\in}X^-_f}{\chi}(c)|L(1,{\chi})|^2$$, where $X^-_f$ is the set of the $\phi$(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to ${\pm}1$ modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c $\in$ {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.

Keywords

L-function;character;mean values;moments

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  1. On the twisted quadratic moment for Dirichlet L-functions vol.174, 2017, https://doi.org/10.1016/j.jnt.2016.11.010