On Li’s Coefficients for Some Classes of L-Functions

Odžak, Almasa. "On Li’s Coefficients for Some Classes of L-Functions." Mathematica Balkanica New Series 24.3-4 (2010): 217-228. <http://eudml.org/doc/11343>.

@article{Odžak2010,
abstract = {AMS Subj. Classification: 11M41, 11M26, 11S40We 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.},
author = {Odžak, Almasa},
journal = {Mathematica Balkanica New Series},
keywords = {Li’s Coefficients; Selberg Class; Rankin-Selberg L-Functions; Generalized Ramanujan Conjecture; Generalized Riemann Hypothesis; Li's coefficients; global L-functions; Generalized Riemann hypothesis},
language = {eng},
number = {3-4},
pages = {217-228},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {On Li’s Coefficients for Some Classes of L-Functions},
url = {http://eudml.org/doc/11343},
volume = {24},
year = {2010},
}

TY - JOUR
AU - Odžak, Almasa
TI - On Li’s Coefficients for Some Classes of L-Functions
JO - Mathematica Balkanica New Series
PY - 2010
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 24
IS - 3-4
SP - 217
EP - 228
AB - AMS Subj. Classification: 11M41, 11M26, 11S40We 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.
LA - eng
KW - Li’s Coefficients; Selberg Class; Rankin-Selberg L-Functions; Generalized Ramanujan Conjecture; Generalized Riemann Hypothesis; Li's coefficients; global L-functions; Generalized Riemann hypothesis
UR - http://eudml.org/doc/11343
ER -