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The Exterior Cube L-Function for GL(6)

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Compositio Mathematica

Abstract

We construct a Rankin Selberg integral to represent the exterior cube L function L(π,Λ3,s) of an automorphic cuspidal module π of GL6(\(\mathbb{A}\) F ) (where F is a number field). We determine the poles of this L function and find period conditions for the special value L(π,Λ3,1/2). We use the Siegal Weil formula. We also state an analogue of the Gross–Prasad conjecture concerning a criterion for the nonvanishing of L(π,Λ3,1/2).

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Authors and Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    David Ginzburg

  2. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, U.S.A.

    Stephen Rallis

Authors
  1. David Ginzburg
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  2. Stephen Rallis
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Ginzburg, D., Rallis, S. The Exterior Cube L-Function for GL(6). Compositio Mathematica 123, 243–272 (2000). https://doi.org/10.1023/A:1002461508749

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  • DOI: https://doi.org/10.1023/A:1002461508749

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