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.
"On Asymptotic Behavior of Generalized Li Coefficients." Taiwanese J. Math. 22 (6) 1321 - 1346, December, 2018. https://doi.org/10.11650/tjm/180407