Higher Derivatives of L-series associated to Real Quadratic Fields

Abstract

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.