bio  website  math.umn.edu/~garrett 

location  US  
age  62  
visits  member for  3 years, 4 months 
seen  1 hour ago  
stats  profile views  4,514 
I am interested in the application of modern analysis to the spectral theory of Eisenstein series and other automorphic forms, Lfunctions, and number theory. This includes representation theory of (mostly reductive) Lie groups and padic groups, and harmonic analysis on these groups and their homogeneous spaces. Necessarily Schwartz' distributions, Sobolev spaces, and similar things play important supporting roles. I find that a mildly categorical viewpoint is very helpful in keeping things straight.
3h

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Is real analytic function good enough (see problem)?
@GHfromMO, I think people "believed in" a "principle of permanence" for some time before the notion of holomorphic function was made explicit. And, more often these days I would call it "the identity principle"... 
6h

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Existence of real modular function with specific behavior as $q\to 0$
@fernando, this construction wouldn't be able to give you a function vanishing along $q=\overline{q}$, anyway, because then the corresponding $f$ would be of absolute value $1$ on the imaginary axis, so couldn't go to $0$ at $i\infty$. But on the compactified modular curve $\isom \mathbb P^1$, giving up the Riemannian structure inherited from the upper halfplane, the $q$ is a local coordinate at the image of $i\infty$, and the fundamental solution for the (spherical) Laplacian on that $\mathbb P^1$ will have a loglike singularity, yes. Is this the sort of thing you want? 
9h

answered  Existence of real modular function with specific behavior as $q\to 0$ 
1d

reviewed  Approve suggested edit on Realworld applications of mathematics, by arxiv subject area? 
Aug 24 
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If the generating function summation and zeta regularized sum of a divergent exist, do they always coincide?
A quibble: The way the first example is worded may give a misleading impression, blurring "taking a limit" with "evaluation of meromorphic continuation at a point". If the meromorphic continuation has the desired point at the edge of the circle of convergence, then a nontangential limit should give the same outcome, yes, but the idea is not restricted to that case... 
Aug 21 
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On the pole of local Lfunction
Another, similar, common misconception is that "local functional equations" should combine to give the "global functional equation", and this is not the case. 
Aug 21 
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Where to find (personal) motivation
@William, yes, in various possible wordings, there are two different things, or at least two different extremes on a spectrum, and accidentally trying (in one's mind) to make them be the same thing surely creates stress of several sorts. At the very least, one can try to remind oneself that, for example, there's "the art/science of mathematics", and then there's "the business of mathematics". 
Aug 20 
answered  Where to find (personal) motivation 
Aug 20 
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Where to find (personal) motivation
Also a rather mixed bag to "appear in Wikipedia"... :) 
Aug 20 
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When is a local subring of a number field a valuation ring?
How is your nonDedekind ring described, then? Is it an "order" of a ring of algebraic integers, for example? If so, then localizing at any prime not dividing the "conductor" will make the localization be the same as the localization of the full ring of algebraic integers... Or what context do you have? 
Aug 20 
answered  When is a local subring of a number field a valuation ring? 
Aug 14 
reviewed  Approve suggested edit on Vanishing of Motivic Cohomology 
Aug 14 
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When is a cubic polynomial a cube?
Because it's cubic, barring various degeneracies it'll be an elliptic curve, and many things are known about rational points (MordellWeil), while integral points are subtler. Searching on "elliptic curve" should give you a broader context. 
Aug 8 
reviewed  Approve suggested edit on citations tag wiki excerpt 
Aug 4 
reviewed  Reject suggested edit on Why are they called Specht Modules? 
Aug 3 
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Multiplicity of automorphic representation
The only discrete spectrum is cuspidal or made from residues of cuspidaldata Eisenstein series. In the continuous spectrum, the same continuous spectrum can occur over and over, but not as genuine subrepresentations. What do you mean to ask about "multiplicities" in the latter case? 
Jul 30 
revised 
Whittaker models for $GL_n$ and Fourier coefficients
added 899 characters in body 
Jul 30 
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Whittaker models for $GL_n$ and Fourier coefficients
@GHfromMO, ah, I hadn't noticed the edit in the question. Thanks... 
Jul 30 
answered  Whittaker models for $GL_n$ and Fourier coefficients 
Jul 30 
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Whittaker models for $GL_n$ and Fourier coefficients
Maybe the transition from character of $\mathbb Q\backslash \mathbb A$ to "generic" character on $N$ could bear some amplification... and, as the questioner anticipates, a onedimensional repn must factor through a quotient group, in this case $N$ by its derived group, etc. 