Bulgarian Academy of Sciences - National Committee for Mathematics
Mathematica Balkanica New Series, Vol. 24, Fasc 3-4 (2010), 217p-228p
We study the generalized Li coeﬃcients associated with the class S♯♭
of functions containing the Selberg class and (unconditionally) the class of all automorphic L-functions attached to irreducible unitary cuspidal representations of GLN(Q) and the class of L-functions attached to the Rankin-Selberg convolution of two unitary cuspidal automorphic representations π and π′ of GLm(AF ) and GLm′ (AF ). We deduce a full asymptotic expansion of the Archimedean contribution to these coeﬃcients and investigate the contribution of the non-archimedean term. Obtained results are applied to automorphic L-functions. Also, a bound towards a generalized Ramanujan conjecture for the Archimedean Langlands parameters µπ(v, j) of π is derived.