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Classical Analysis
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
2014/10/29
16:00-17:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Eric Stade (University of Colorado Boulder)
Whittaker functions and Barnes-Type Lemmas (ENGLISH)
Eric Stade (University of Colorado Boulder)
Whittaker functions and Barnes-Type Lemmas (ENGLISH)
[ Abstract ]
In the theory of automorphic forms on GL(n,R), which concerns harmonic analysis and representation theory of this group, certain special functions known as GL(n,R) Whittaker functions play an important role. These Whittaker functions are generalizations of classical Whittaker (or, more specifically, Bessel) functions.
Mellin transforms of products of GL(n,R) Whittaker functions may be expressed as certain Barnes type integrals, or equivalently, as hypergeometric series of unit argument. The general theory of automorphic forms predicts that these Mellin transforms reduce, in certain cases, to products of gamma functions. That this does in fact occur amounts to a whole family of generalizations of the so-called Barnes' Lemma and Barnes' Second Lemma, from the theory of hypergeometric series. We will explore these generalizations in this talk.
This talk will not require any specific knowledge of automorphic forms.
In the theory of automorphic forms on GL(n,R), which concerns harmonic analysis and representation theory of this group, certain special functions known as GL(n,R) Whittaker functions play an important role. These Whittaker functions are generalizations of classical Whittaker (or, more specifically, Bessel) functions.
Mellin transforms of products of GL(n,R) Whittaker functions may be expressed as certain Barnes type integrals, or equivalently, as hypergeometric series of unit argument. The general theory of automorphic forms predicts that these Mellin transforms reduce, in certain cases, to products of gamma functions. That this does in fact occur amounts to a whole family of generalizations of the so-called Barnes' Lemma and Barnes' Second Lemma, from the theory of hypergeometric series. We will explore these generalizations in this talk.
This talk will not require any specific knowledge of automorphic forms.
