A New Regularized Siegel-Weil Type Formula. Part I

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Abstract

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.

Original languageEnglish
Pages (from-to)60-112
Number of pages53
JournalGeometric and Functional Analysis
Volume34
Issue number1
DOIs
StatePublished - Feb 2024

Keywords

  • Eisenstein series
  • L-functions
  • Siegel-Weil formula
  • Speh representations

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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