Higher Derivatives of L-series associated to Real Quadratic Fields

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
30 Pages. Adapted from a chapter of the author's PhD thesis

Keywords

Number Theory, 11R42

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/119872

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0612189
 http://arxiv.org/abs/math/0612189

Collections

arXiv