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THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET $L$-FUNCTIONS OVER RATIONAL FUNCTION FIELDS

Part of: Zeta and $L$-functions: analytic theory Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  28 August 2018

GORAN DJANKOVIĆ Open the ORCID record for GORAN DJANKOVIĆ [Opens in a new window]
GORAN DJANKOVIĆ*
Affiliation:
Faculty of Mathematics, University of Belgrade, Studentski Trg 16, p.p. 550, 11000 Belgrade, Serbia email djankovic@matf.bg.ac.rs
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Abstract

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We prove the reciprocity law for the twisted second moments of Dirichlet $L$-functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet $L$-functions over $\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet $L$-functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law for the twisted second moment of Dirichlet $L$-functions’, Forum Math. 23(6) (2011), 1323–1337].

Keywords

momentstwisted reciprocityDirichlet L-functionfunction field

MSC classification

Primary: 11M38: Zeta and $L$-functions in characteristic $p$
Secondary: 11T06: Polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 383 - 388
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work was partially supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, Project no. 174008.

References

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Conrey, J. B., ‘The mean-square of Dirichlet $L$ -functions’, arXiv:0708.2699 [math.NT] (2007).Google Scholar
Rosen, M., Number Theory in Function Fields, Graduate Texts in Mathematics, 210 (Springer, New York, NY, 2000).Google Scholar
Young, M. P., ‘The reciprocity law for the twisted second moment of Dirichlet L-functions’, Forum Math. 23(6) (2011), 1323–1337.Google Scholar