Open Access
December, 2018 On Asymptotic Behavior of Generalized Li Coefficients
Anne-Maria Ernvall-Hytönen, Almasa Odžak, Medina Sušić
Taiwanese J. Math. 22(6): 1321-1346 (December, 2018). DOI: 10.11650/tjm/180407


In this paper, we consider the asymptotic behaviour of $\tau$-Li coefficients for the wide class of $L$-functions that contains the Selberg class, the class of all automorphic $L$-functions, the Rankin-Selberg $L$-functions, as well as products of suitable shifts of the mentioned functions. We consider both archimedean and non-archimedean contribution to the $\tau$-Li coefficients, both separately, and their joint contribution to the coefficients. We also derive the behavior of the coefficients in the case the $\tau/2$-Riemann hypothesis holds, which is the generalization of the Riemann hypothesis for the class under consideration. Finally, we conclude with some examples and numerics.


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Anne-Maria Ernvall-Hytönen. Almasa Odžak. Medina Sušić. "On Asymptotic Behavior of Generalized Li Coefficients." Taiwanese J. Math. 22 (6) 1321 - 1346, December, 2018.


Received: 1 February 2018; Revised: 17 April 2018; Accepted: 26 April 2018; Published: December, 2018
First available in Project Euclid: 21 May 2018

zbMATH: 07021692
MathSciNet: MR3880235
Digital Object Identifier: 10.11650/tjm/180407

Primary: 11M26 , 11M41

Keywords: $L$-functions , generalized Li coefficients

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 6 • December, 2018
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