TY - JOUR
T1 - A New Regularized Siegel-Weil Type Formula. Part I
AU - Ginzburg, David
AU - Soudry, David
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/2
Y1 - 2024/2
N2 - In this paper, we prove a formula, realizing certain residual Eisenstein series on symplectic groups as regularized kernel integrals. These Eisenstein series, as well as the kernel integrals, are attached to Speh representations. This forms an initial step to a new type of a regularized Siegel-Weil formula that we propose. This new formula bears the same relation to the generalized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan, as does the regularized Siegel-Weil formula to the doubling integrals of Piatetski-Shapiro and Rallis.
AB - In this paper, we prove a formula, realizing certain residual Eisenstein series on symplectic groups as regularized kernel integrals. These Eisenstein series, as well as the kernel integrals, are attached to Speh representations. This forms an initial step to a new type of a regularized Siegel-Weil formula that we propose. This new formula bears the same relation to the generalized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan, as does the regularized Siegel-Weil formula to the doubling integrals of Piatetski-Shapiro and Rallis.
KW - Eisenstein series
KW - L-functions
KW - Siegel-Weil formula
KW - Speh representations
UR - http://www.scopus.com/inward/record.url?scp=85182849463&partnerID=8YFLogxK
U2 - 10.1007/s00039-024-00657-y
DO - 10.1007/s00039-024-00657-y
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AN - SCOPUS:85182849463
SN - 1016-443X
VL - 34
SP - 60
EP - 112
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 1
ER -