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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 296, Pages 123–132
DOI: https://doi.org/10.1134/S0371968517010095 (Mi tm3780) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

J. Kaczorowskiab, A. Perellic

a Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
b Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland
c Dipartimento di Matematica, Universitá di Genova, Genova, Italy
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DOI: https://doi.org/10.1134/S0371968517010095
Abstract: Let $\chi \pmod q$, $q>1$, 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.
Funding agency Grant number
Istituto Nazionale di Alta Matematica "Francesco Severi"
Ministero dell'Istruzione, dell'Università e della Ricerca PRIN2015
National Science Centre (Narodowe Centrum Nauki) 2013/11/B/ST1/02799
This research was partially supported by Istituto Nazionale di Alta Matematica, by grant PRIN2015 Number Theory and Arithmetic Geometry and by grant no. 2013/11/B/ST1/02799 Analytic Methods in Arithmetic of the National Science Centre.
Received: May 2, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 296, Pages 115–124
DOI: https://doi.org/10.1134/S0081543817010096
Bibliographic databases:
Document Type: Article
UDC: 511.331
Language: Russian
Citation: J. Kaczorowski, A. Perelli, “A note on Linnik's approach to the Dirichlet $L$-functions”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 123–132; Proc. Steklov Inst. Math., 296 (2017), 115–124
Citation in format AMSBIB
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\by J.~Kaczorowski, A.~Perelli
\paper A note on Linnik's approach to the Dirichlet $L$-functions
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 296
\pages 123--132
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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