Oct. 18, 2004, Monday, 10:10-11:00am. Vincent 203a ********************** Steve Miller, Rugers University Title: On the Analytic Continuation of the Exterior Square L-function Abstract: Both integral representations and the Langlands-Shahidi method give detailed information about the analytic properties of various automorphic L-functions. However, in most cases this information is unfortunately not complete in practice. For example, integral representations are often produced which are entire, but which are not completely identified with their targeted Langlands L-function. On the other hand, the Langlands-Shahidi method produces the desired functional equation, but in some cases does not rule out having unwanted poles. We have pursued a third method, that of pairing automorphic distributions over flag varieties. It is formally similar to the method of integral representations, but instead derives holomorphy from oscillatory properties of distributions rather than the rapid decay of cusp forms. As a test case the method gives new examples of the full holomorphic continuation of the exterior square L-functions on GL(n) that were not obtained by the previous methods. The talk will focus on the notion of automorphic distribution and these examples of the exterior square. (Joint work with Wilfried Schmid) ######################################################################