1. On the zeros of Dirichlet -functions
- Author
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Raouf Ouni, Kamel Mazhouda, and Sami Omar
- Subjects
Mathematical society ,General Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Dirichlet distribution ,010101 applied mathematics ,Riemann hypothesis ,symbols.namesake ,Number theory ,Computational Theory and Mathematics ,symbols ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
This paper [1], which was published online on 1 June 2011, has been retracted by agreement between the authors, the journal’s Editor-in-Chief Derek Holt, the London Mathematical Society and Cambridge University Press.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.)
- Published
- 2011