An analog of theta-lifting for a curve over dual numbers over a finite field

David Kazhdan; Alexander Polishchuk

doi:10.4310/PAMQ.260624215953

An analog of theta-lifting for a curve over dual numbers over a finite field

David Kazhdan
, Alexander Polishchuk

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We continue the study of automorphic functions associated with a curve C over the ring k[ϵ]/(ϵ²), where k is a finite field, begun in [3]. More precisely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) introduced in [3]. We prove that all strongly cuspidal functions in S(SL₂(F)\SL₂(A_C)) can be constructed using theta-lifting for an appropriate double covering^˜C → C.

Original language	English
Pages (from-to)	1115-1166
Number of pages	52
Journal	Pure and Applied Mathematics Quarterly
Volume	22
Issue number	3
DOIs	https://doi.org/10.4310/PAMQ.260624215953
State	Published - 2026

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© 2026, International Press, Inc.. All rights reserved.

Keywords

Theta-lifting
automorphic function

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10.4310/PAMQ.260624215953

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An analog of theta-lifting for a curve over dual numbers over a finite field

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