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


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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.

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J. Kaczorowski

Faculty of Mathematics and Computer Science; Institute of Mathematics of the Polish Academy of Sciences

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Email: kjerzy@amu.edu.pl
波兰, ul. Umultowska 87, Poznań, 61-614; ul. Śniadeckich 8, Warsaw, 00-656

A. Perelli

Dipartimento di Matematica

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Email: perelli@dima.unige.it
意大利, via Dodecaneso 35, Genova, 16146

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