2006/12/07 by Lawrence Taylor, Taylor, Lawrence
Mathematics · #11R42 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11R42
paper · pdf · doi:10.48550/arxiv.math/0612189
30 Pages. Adapted from a chapter of the author's PhD thesis
arxiv created 2006/12/07 · openalex publication_date 2006/12/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Previously we developed a nontrivial notion of line bundles over Quantum Tori. In this text we study sections of these line bundles leading to a study concerning theta functions for Quantum Tori. We prove the existence of such meromorphic theta functions, and view their application in the context of Stark's conjectures and Hilbert's twelfth problem. Generalising the work of Shintani, we show that (modulo a certain conjecture) we can write the derivatives of L-series associated to Real Quadratic Fields in terms of special values of theta functions over Quantum Tori.