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The Exterior Cube L-Function for GL(6)

Published online by Cambridge University Press:  04 December 2007

David Ginzburg  and
Stephen Rallis
David Ginzburg
Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Stephen Rallis
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, U.S.A.
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Abstract

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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(${\Bbb A}$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).

Keywords

Rankin-Selberg integralpoles of L functionsspecial value of L functions
Type
Research Article
Information
Compositio Mathematica , Volume 123 , Issue 3 , September 2000 , pp. 243 - 272
Copyright
© 2000 Kluwer Academic Publishers