Symmetries for Siegel Theta Functions, Borcherds Lifts and Automorphic Green Functions

2010/03/11 by Bernhard Heim, Heim, Bernhard, Atsushi Murase +1
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Automorphic form #FOS: Mathematics #Geometry #Group (periodic table) #Homogeneous space #Mathematics #Modular form #Number Theory (math.NT) #Physics #Pure mathematics #Quadratic equation #Quantum mechanics #Siegel modular form #Signature (topology) #Theta function #math.NT

paper · pdf · doi:10.48550/arxiv.1003.2248

22 pages

arxiv created 2010/03/11 · openalex publication_date 2010/03/11 · arxiv updated 2010/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Let q be an integral quadratic form of signature (2,m+2). We will show that the Siegel theta functions attached to q satisfies certain symmetries. As an application, we prove the symmetries for automorphic forms on the orthogonal group of q closely related to Heegener divisors (Borcherds lifts and automorphic Green functions).

Citations

• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Algebras, BPS states, and strings
• Heegner points and derivatives ofL-series
• On the Spezialschar of Maass

Related

• On the regularized Siegel-Weil formula (the second term identity) and non-vanishing of theta lifts from orthogonal groups
• Siegel theta series for quadratic forms of signature (m-1,1)
• Higher Siegel theta lifts on Lorentzian lattices, harmonic Maass forms, and Eichler-Selberg type relations
• Regularized theta lifts for orthogonal groups over totally real fields
• On Two Geometric Theta Lifts