A note on Linnik’s approach to the Dirichlet L-functions

Аннотация

Abstract—Let χ (mod q), q > 1, be a primitive Dirichlet character. We first present a detailed account of Linnik’s deduction of the functional equation of L(s, χ) from the functional equation of ζ(s). Then we show that the opposite deduction can be obtained by a suitable modification of the method, involving finer arithmetic arguments.