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On the zeros of Dirichlet $L$-functions

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  01 May 2018

Sami Omar ,
Raouf Ouni  and
Kamel Mazhouda
Sami Omar
Affiliation:
Department of Mathematics, King Khalid University, Abha 9004, Saudi Arabia Department of Mathematics, Faculty of Science of Tunis, 2092 Tunis, Tunisia email sami.omar@fst.rnu.tn
Raouf Ouni
Affiliation:
Department of Mathematics, Faculty of Science of Tunis, 2092 Tunis, Tunisia email raouf.ouni@fst.rnu.tn
Kamel Mazhouda
Affiliation:
Department of Mathematics, Faculty of Science of Monastir, 5000 Monastir, Tunisia email kamel.mazhouda@fsm.rnu.tn

Abstract

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This paper [1], which was published online on 1 June 2011, has been retracted by agreement between the authors, the journal’s Editor-in-Chief Derek Holt, the London Mathematical Society and Cambridge University Press. The retraction was agreed to prevent other authors from using incorrect mathematical results. (In this paper, we compute and verify the positivity of the Li coefficients for the Dirichlet $L$-functions using an arithmetic formula established in Omar and Mazhouda, J. Number Theory 125 (2007) no. 1, 50–58; J. Number Theory 130 (2010) no. 4, 1109–1114. Furthermore, we formulate a criterion for the partial Riemann hypothesis and we provide some numerical evidence for it using new formulas for the Li coefficients.)

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 140 - 154
Copyright
© The Author(s) 2011 

References

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