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Turkish Journal of Mathematics

Authors

ALMASA ODZAK

DOI

10.3906/mat-1410-41

Abstract

We investigate relations between zero-free regions of certain $L$-functions and the asymptotic behavior of corresponding generalized Li coefficients. Precisely, we prove that violation of the $\tau/2$-generalized Riemann hypothesis implies oscillations of corresponding $\tau$-Li coefficients with exponentially growing amplitudes. Results are obtained for class $\shfs$ that contains the Selberg class, the class of all automorphic $L$-functions, the Rankin--Selberg $L$-functions, and products of suitable shifts of the mentioned functions.

First Page

688

Last Page

702

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