Test Schwartz functions at p for theta lifts of Hida families

2025/10/24 by Liu, Zheng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.21644

Abstract

We construct Hida families of theta lifts from definite orthogonal and unitary groups. A major ingredient of the construction is the choice of test Schwartz functions at places dividing p. We select a special type of Schwartz functions endowed with the equivariance property for the action of \mathbbU_p-operators.

Citations

• Bushnell-Kutzko types for P-ordinary automorphic representations on unitary groups
• Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on GU(3,1)
• Iwasawa Main Conjecture for Rankin-Selberg p-adic L-functions: Non-Ordinary Case

Related

• Hida family of theta lift from U(1) to definite U(2)
• Theta lifting for discrete series representations of real unitary groups
• Regularized theta lifts for orthogonal groups over totally real fields
• p-adic L-functions for P-ordinary Hida families on unitary groups
• Theta lifting for tempered representations of real unitary groups