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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University, 62901, Carbondale, IL, USA

    Henry H. Kim

  2. Department of Mathematics, Purdue University, 47907-1395, West Lafayette, IN, USA

    Freydoon Shahidi

Authors
  1. Henry H. Kim
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  2. Freydoon Shahidi
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Correspondence to Henry H. Kim.

Additional information

Partially supported by NSF grant DMS9610387.

Partially supported by NSF grant DMS9970156.

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Kim, H.H., Shahidi, F. Holomorphy of Rankin tripleL-functions; special values and root numbers for symmetric cubeL-functions. Isr. J. Math. 120, 449–466 (2000). https://doi.org/10.1007/BF02834847

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  • DOI: https://doi.org/10.1007/BF02834847

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