TY - JOUR
T1 - Cusp forms on GSp(4) with SO(4)-periods
AU - Flicker, Yuval Z.
PY - 2011/6
Y1 - 2011/6
N2 - The SaitoKurokawa lifting of automorphic representations from PGL(2) to the projective symplectic group of similitudes PGSp(4) of genus 2 is studied using the Fourier summation formula (an instance of the "relative trace formula"), thus characterizing the image as the representations with a nonzero period for the special orthogonal group SO(4, E/F) associated to a quadratic extension E of the global base field F, and a nonzero Fourier coefficient for a generic character of the unipotent radical of the Siegel parabolic subgroup. The image is nongeneric and almost everywhere nontempered, violating a naive generalization of the Ramanujan conjecture. Technical advances here concern the development of the summation formula and matching of relative orbital integrals.
AB - The SaitoKurokawa lifting of automorphic representations from PGL(2) to the projective symplectic group of similitudes PGSp(4) of genus 2 is studied using the Fourier summation formula (an instance of the "relative trace formula"), thus characterizing the image as the representations with a nonzero period for the special orthogonal group SO(4, E/F) associated to a quadratic extension E of the global base field F, and a nonzero Fourier coefficient for a generic character of the unipotent radical of the Siegel parabolic subgroup. The image is nongeneric and almost everywhere nontempered, violating a naive generalization of the Ramanujan conjecture. Technical advances here concern the development of the summation formula and matching of relative orbital integrals.
KW - Fourier summation formula
KW - Periods of automorphic forms
KW - SaitoKurokawa lifting
KW - fundamental lemma
KW - relative orbital integrals
KW - symplectic group
UR - http://www.scopus.com/inward/record.url?scp=79959480010&partnerID=8YFLogxK
U2 - 10.1142/S1793042111004186
DO - 10.1142/S1793042111004186
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:79959480010
SN - 1793-0421
VL - 7
SP - 855
EP - 919
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 4
ER -