1999/09/27 by Olav K. Richter · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Modular form #Symplectic geometry #Mathematics #Pure mathematics #Quadratic equation #Root (linguistics) #Theta function #Modular design #Algebra over a field #Computer science #Geometry
paper · pdf · doi:10.1090/s0002-9939-99-05619-1
openalex publication_date 1999/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.