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 language | English |
---|---|
Title of host publication | Hypergeometry, Integrability and Lie Theory - Virtual Conference Hypergeometry, Integrability and Lie Theory, 2020 |
Editors | Erik Koelink, Stefan Kolb, Nicolai Reshetikhin, Bart Vlaar |
Publisher | American Mathematical Society |
Pages | 1-27 |
Number of pages | 27 |
ISBN (Print) | 9781470465209 |
DOIs | |
State | Published - 2022 |
Event | Virtual conference on Hypergeometry, Integrability and Lie Theory, 2020 - Virtual, Online Duration: 7 Dec 2020 → 11 Dec 2020 |
Publication series
Name | Contemporary Mathematics |
---|---|
Volume | 780 |
ISSN (Print) | 0271-4132 |
ISSN (Electronic) | 1098-3627 |
Conference
Conference | Virtual conference on Hypergeometry, Integrability and Lie Theory, 2020 |
---|---|
City | Virtual, Online |
Period | 7/12/20 → 11/12/20 |
Bibliographical note
Publisher Copyright:© 2022 American Mathematical Society.