Explicit formula for the (GL₂, GL₂) theta lift via Bruhat decomposition

2024/09/11 by Wei Xu, Xu, Peter
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced NMR Techniques and Applications #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.06940

openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using combinations of weight-1 and weight-2 of Kronecker-Eisenstein series to construct currents in the distributional de Rham complex of a squared elliptic curve, we find a simple explicit formula for the type II (GL₂, GL₂) theta lift without smoothing, analogous to the classical formula of Siegel for periods of Eisenstein series. For K a CM field, the same technique applies without change to obtain an analogous formula for the (GL₂(K),K^×) theta correspondence.

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