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Israel Journal of Mathematics

, Volume 120, Issue 2, pp 449–466 | Cite as

Holomorphy of Rankin tripleL-functions; special values and root numbers for symmetric cubeL-functions

  • Henry H. Kim
  • Freydoon Shahidi
Article

Abstract

In this paper we prove the holomorphy of Rankin tripleL-functions for three cusp forms on GL(2) on the entire complex plane, if at least one of them is non-monomial. We conclude the paper by proving the equality of our root numbers for the third and the fourth symmetric powerL-functions with those of Artin through the local Langlands correspondence. We also revisit Deligne’s conjecture on special values of symmetric cubeL-functions.

Keywords

Modular Form Parabolic Subgroup Eisenstein Series Cusp Form Root Number 
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Copyright information

© Hebrew University of Jerusalem 2000

Authors and Affiliations

  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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