Email this article A note on Linnik’s approach to the Dirichlet L-functions
- Authors: Kaczorowski J.1,2, Perelli A.3
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Affiliations:
- Faculty of Mathematics and Computer Science
- Institute of Mathematics of the Polish Academy of Sciences
- Dipartimento di Matematica
- Issue: Vol 296, No 1 (2017)
- Pages: 115-124
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/174213
- DOI: https://doi.org/10.1134/S0081543817010096
- ID: 174213
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Abstract
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.
About the authors
J. Kaczorowski
Faculty of Mathematics and Computer Science; Institute of Mathematics of the Polish Academy of Sciences
Author for correspondence.
Email: kjerzy@amu.edu.pl
Poland, ul. Umultowska 87, Poznań, 61-614; ul. Śniadeckich 8, Warsaw, 00-656
A. Perelli
Dipartimento di Matematica
Author for correspondence.
Email: perelli@dima.unige.it
Italy, via Dodecaneso 35, Genova, 16146
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