Characteristic functions of p-adic integral operators

Pavel Etingof, David Kazhdan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Let P ∈ Qp [x, y], s ∈ C with sufficiently large real part, and consider the integral operator ∫ 1 (AP,sf)(y):= 1 − p−1 |P (x, y)|sf(x)|dx| Zp on L2(Zp). We show that if P is homogeneous of degree d then for each character χ of Z×p the characteristic function det(1 − uAP,s,χ) of the restriction AP,s,χ of AP,s to the eigenspace L2(Zp)χ is the q-Wronskian of a set of solutions of a (possibly confluent) q-hypergeometric equation, where q = p−1−ds . In particular, the nonzero eigenvalues of AP,s,χ are the reciprocals of the zeros of such q-Wronskian.

Original languageEnglish
Title of host publicationHypergeometry, Integrability and Lie Theory - Virtual Conference Hypergeometry, Integrability and Lie Theory, 2020
EditorsErik Koelink, Stefan Kolb, Nicolai Reshetikhin, Bart Vlaar
PublisherAmerican Mathematical Society
Pages1-27
Number of pages27
ISBN (Print)9781470465209
DOIs
StatePublished - 2022
EventVirtual conference on Hypergeometry, Integrability and Lie Theory, 2020 - Virtual, Online
Duration: 7 Dec 202011 Dec 2020

Publication series

NameContemporary Mathematics
Volume780
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceVirtual conference on Hypergeometry, Integrability and Lie Theory, 2020
CityVirtual, Online
Period7/12/2011/12/20

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society.

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