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]LNNNNNN$=1rrLLLL@MGLDear editors:
I am Wei Ren and am currently a sophomore at Colgate University, Hamilton, NY.
I am submitting the research paper I did last summer to be published in the RHIT
Mathematics Journal. This was a summer research project sponsored by the
Division of Natural Science and Mathematics of Colgate University, which started
last May and was completed July, 2001. I just finished my freshman year of
college at the time I started my research. My advisor for this project was
Professor Scott Ahlgren, who is now a professor at UIUC. I plan to do more
research with faculty members of Colgate in the near future; my ultimate goal is
to pursue a doctorate degree in mathematics.
Please note that Professor Ahlgren will send his letter of support soon.
Enc. Identities.tex (my paper in AmsTex format) and Abstract.txt (my abstract for
the paper as plain text)
Wei Ren
January 21, 2002
**********
Dear Editors,
I am writing in support of the paper
``Three term identities for the coefficients of certain
infinite
products'' which has just been submitted by Wei Ren of
Colgate University.
I was an assistant professor at Colgate University from
1998-2000;
I am currently an assistant professor at the University of
Illinois
at Urbana-Champaign.
Wei worked on this project under my supervision last
summer;
this was the summer between his freshman and sophomore
years
in college.
In a recent paper, Farkas and Kra use function-theoretic
methods to obtain some identities involving
the coefficients of certain infinite products.
They ask whether their identities are special cases of
more general identities. Using the theory of modular forms
and properties of Dedekind's eta-function, Wei was able
to show that each of the original identities is just
one of an infinite family of identities.
In my opinion this is very solid work for an undergraduate.
(To be honest, I should say that to experts in the field
of modular forms these results will not be surprising.)
The results are clean and easily stated and the paper is
very well
written. However to prove the results, as you can see from
the paper,
requires a good understanding of the basic theory of
modular forms
as well as some technical proficiency. The level of this
work
is well above the standard undergraduate curriculum, and I
think it is
is truly exceptional for a freshman.
In summary, this is undergraduate work
of very high quality, and I very strongly recommend
publication.
Please feel free to contact me if you require any
additional information.
Sincerely,
Scott Ahlgren
Department of Mathematics
University of Illinois
Urbana, IL 61801
ahlgren@math.uiuc.edu
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