A New Regularized Siegel-Weil Type Formula. Part I

David Ginzburg, David Soudry*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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

Funding

FundersFunder number
Israel Science Foundation295/22
Porter School of Environmental Studies, Tel Aviv University
Tel Aviv University
Claire and Amédée Maratier Institute for the Study of Blindness and Visual Disorders, Tel Aviv University
Center for Nanoscience and Nanotechnology, Tel Aviv University
Adams Super Center for Brain Studies,Tel Aviv University
Cancer Biology Research Center, Tel Aviv University
Varda and Boaz Dotan Research Center for Hemato-Oncology Research, Tel Aviv University
Manna Center for Plant Biosciences, Tel Aviv University
Sagol School of Neuroscience, Tel Aviv University
Check Point Institute for Information Security, Tel Aviv University
Yitzhak and Chaya Weinstein Research Institute for Signal Processing, Tel Aviv University

    Keywords

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

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