Oct. 18, 2004, Monday, 10:10-11:00am.

Vincent 203a

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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)

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