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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
