Abstract
In this paper we obtain a full asymptotic expansion of the archimedean contribution to the Li coefficients λF(−n) (n is a positive integer) attached to a function F in the certain class S♯♭ of functions containing the Selberg class S and (unconditionally) the class of all automorphic L-functions attached to irreducible, unitary cuspidal representations of GLN(Q). Applying the obtained results to automorphic L-functions, we improve the result of J.C. Lagarias concerning the asymptotic behavior of archimedean contribution to the nth Li coefficient attached to the automorphic L-function. We also deduce asymptotic behaviors of λF(−n), as n→+∞ equivalent to Generalized Riemann Hypothesis (GRH) true and GRH false for F∈S♯♭.
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.
