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On asymptotic behavior of generalized Li coefficients. (English) Zbl 1429.11172
Summary: 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.
##### MSC:
 11M41 Other Dirichlet series and zeta functions 11M26 Nonreal zeros of $$\zeta (s)$$ and $$L(s, \chi)$$; Riemann and other hypotheses
##### Keywords:
$$L$$-functions; generalized Li coefficients
Arb
Full Text:
##### References:
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