Let $chi$ (mod $q$), $q>1$, be a primitive Dirichlet character. We first present a detailed account of Linnik's deduction of the functional equation of $L(s,chi)$ from the functional equation of $zeta(s)$. Then we show that the opposite deduction can be obtained by a suitable modification of the method, involving finer arithmetic arguments.
A note on Linnik’s approach to the Dirichlet L-functions
PERELLI, ALBERTO
2017-01-01
Abstract
Let $chi$ (mod $q$), $q>1$, be a primitive Dirichlet character. We first present a detailed account of Linnik's deduction of the functional equation of $L(s,chi)$ from the functional equation of $zeta(s)$. Then we show that the opposite deduction can be obtained by a suitable modification of the method, involving finer arithmetic arguments.
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