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2017 On the $\tau $-Li coefficients for automorphic $L$-functions
Kamel Mazhouda
Rocky Mountain J. Math. 47(6): 1987-2011 (2017). DOI: 10.1216/RMJ-2017-47-6-1987

Abstract

In this paper, we extend the Li coefficients for automorphic $L$-functions and the Li criterion for the Riemann hypothesis to yield a necessary and sufficient condition for the existence of zero-free strips for automorphic $L$-functions inside the critical strip. Next, we give an arithmetical and asymptotical formula for these coefficients. Finally, we show that there exists an entire function of exponential type that interpolates the extended Li coefficients (or the $\tau $-Li coefficients) at integer values. The results of this paper arise from ideas of the author~\cite {15}, Freitas~\cite {8}, Lagarias~\cite {10} and Odz$\breve {a}$k and Smajlovi$\grave {c}$~\cite {17}.

Citation

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Kamel Mazhouda. "On the $\tau $-Li coefficients for automorphic $L$-functions." Rocky Mountain J. Math. 47 (6) 1987 - 2011, 2017. https://doi.org/10.1216/RMJ-2017-47-6-1987

Information

Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 06816579
MathSciNet: MR3725253
Digital Object Identifier: 10.1216/RMJ-2017-47-6-1987

Subjects:
Primary: 11M06 , 11M36 , 11M41

Keywords: automorphic $L$-functions , Dirichlet series , Li's criterion , Riemann hypothesis

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 6 • 2017
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