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1. 12. 2018.
On Asymptotic Behavior of Generalized Li Coefficients
Abstract. In this paper, we consider the asymptotic behaviour of τ -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 τ -Li coefficients, both separately, and their joint contribution to the coefficients. We also derive the behavior of the coefficients in the case the τ/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.