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Dissertation Information for George Stade

NAME:
- George Stade
- (Alias) George Eric Stade

DEGREE:
- Ph.D.

DISCIPLINE:
- Mathematics

SCHOOL:
- Columbia University (USA) (1988)

ADVISORS:
- None

COMMITTEE MEMBERS:
- None

MPACT Status: Incomplete - Inspected

Title: Whittaker functions and Poincare series for GL

Abstract: "In this thesis we study Poincare series for $GL$($n$, R) that are automorphic for $GL(n$, Z). Specifically, we consider Poincare series constructed from $GL(n$, R) ""Whittaker functions."" Our emphasis will be on the case $n$ = 3.

We will review first some known results in the case of $GL$(2, R). Here our Poincare series is dependent on a single complex variable $\nu$, and is absolutely convergent for values of $\nu$ in a certain half-plane. The series then possesses a meromorphic continuation, as well as functional equation, in the variable $\nu$.

For groups of higher rank, and in particular when $n$ = 3, the situation is fundamentally different. In fact we will see that, for such groups, our Poincare series do not ever converge! Nor does it seem possible to define these series as distributions.

Nevertheless we will attach a meaning to these series, at least in the case $n$ = 3, as the analytic continuation (in a new variable $\mu$) of a linear functional defined on any finite-dimensional space of cusp forms. In this context we will then find a meromorphic continuation and functional equation analogous to those obtained in the case of $GL$(2, R).

We will conclude by indicating the possibilities for extension of our theory to $GL(n$, R)."

MPACT Scores for George Stade

A = 0
C = 1
A+C = 1
T = 0
G = 0
W = 0
TD = 0
TA = 0
calculated 2008-01-31 06:32:51

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