Abstract
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.
Citation
Anne-Maria Ernvall-Hytönen. Almasa Odžak. Medina Sušić. "On Asymptotic Behavior of Generalized Li Coefficients." Taiwanese J. Math. 22 (6) 1321 - 1346, December, 2018. https://doi.org/10.11650/tjm/180407
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