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On the modularity of the GL2-twisted spinor L-function

On the modularity of the GL2-twisted spinor L-function In modern number theory there are famous theorems on the modularity of Dirichlet series attached to geometric or arithmetic objects. There is Hecke’s converse theorem, Wiles proof of the Taniyama-Shimura conjecture, and Fermat’s Last Theorem to name a few. In this article in the spirit of the Langlands philosophy we raise the question on the modularity of the GL2-twisted spinor L-function Z G ⊗ h (s) related to automorphic forms G,h on the symplectic group GSp2 and GL2. This leads to several promising results and finally culminates into a precise very general conjecture. This gives new insights into the Miyawaki conjecture on spinor L-functions of modular forms. We indicate how this topic is related to Ramakrishnan’s work on the modularity of the Rankin-Selberg L-series. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

On the modularity of the GL2-twisted spinor L-function

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Mathematisches Seminar der Universität Hamburg and Springer
Subject
Mathematics; Geometry ; Topology; Number Theory; Combinatorics; Differential Geometry; Algebra
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-009-0028-x
Publisher site
See Article on Publisher Site

Abstract

In modern number theory there are famous theorems on the modularity of Dirichlet series attached to geometric or arithmetic objects. There is Hecke’s converse theorem, Wiles proof of the Taniyama-Shimura conjecture, and Fermat’s Last Theorem to name a few. In this article in the spirit of the Langlands philosophy we raise the question on the modularity of the GL2-twisted spinor L-function Z G ⊗ h (s) related to automorphic forms G,h on the symplectic group GSp2 and GL2. This leads to several promising results and finally culminates into a precise very general conjecture. This gives new insights into the Miyawaki conjecture on spinor L-functions of modular forms. We indicate how this topic is related to Ramakrishnan’s work on the modularity of the Rankin-Selberg L-series.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals

Published: Jul 4, 2009

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