Compositio Mathematica

The Exterior Cube L-Function for GL(6)

David Ginzburg a1 and Stephen Rallis a2
a1 School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
a2 Department of Mathematics, The Ohio State University, Columbus, OH 43210, U.S.A.

Article author query
ginzburg d   [Google Scholar] 
rallis s   [Google Scholar] 


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).

Key Words: Rankin-Selberg integral; poles of L functions; special value of L functions.