The Exterior Cube L-Function for GL(6) |
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| Authors: | David Ginzburg Stephen Rallis |
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| Institution: | (1) School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel;(2) Department of Mathematics, The Ohio State University, Columbus, OH, 43210, U.S.A. |
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| Abstract: | We construct a Rankin Selberg integral to represent the exterior cube L function L( , 3,s) of an automorphic cuspidal module of GL6(
F
) (where F is a number field). We determine the poles of this L function and find period conditions for the special value L(,3,1/2). We use the Siegal Weil formula. We also state an analogue of the Gross–Prasad conjecture concerning a criterion for the nonvanishing of L(,3,1/2). |
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| Keywords: | Rankin-Selberg integral poles of L functions special value of L functions |
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