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Title: On Li’s Coefficients for Some Classes of L-Functions
Authors: Odžak, Almasa
Keywords: Li’s Coefficients
Selberg Class
Rankin-Selberg L-Functions
Generalized Ramanujan Conjecture
Generalized Riemann Hypothesis
Issue Date: 2010
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 24, Fasc 3-4 (2010), 217p-228p
Abstract: 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.
Description: AMS Subj. Classification: 11M41, 11M26, 11S40
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 24, 2010, Fasc. 3-4

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