On the mean square value of the Dirichlet L-function at positive integers
Tom 189 / 2019
Acta Arithmetica 189 (2019), 367-379
MSC: Primary 11M06; Secondary 33B10.
DOI: 10.4064/aa180117-15-7
Opublikowany online: 3 June 2019
Streszczenie
We express the mean square value of the Dirichlet L-function at positive integers as a linear combination of its values at even numbers and for a principal character. The method we take is to construct a connection between a special kind of trigonometric functions and the Dirichlet L-function. Since the coefficients of the linear combination satisfy computable recursion formulae, we can obtain the exact mean square value of the Dirichlet L-function using mathematical software.
