Students Working Seminar in Number Theory
For slides and supplementary material please go to: http://www.math.tamu.edu/~alperen/wsdm.html

Date Time 
Location  Speaker 
Title – click for abstract 

02/03 4:00pm 
Bloc 605AX 
Jiakun Pan Texas A&M University 
Eisenstein series attached to cusps
Continuing the last talk, I will introduce singularity of cusps and
Eisenstein series attached to them. For application, I will also show
how to perform regularized integrals of products of Eisenstein series. 

02/10 4:00pm 
Bloc605ax 
WeiLun Tsai Texas A&M University 
Prime number theoryfrom GL(2) to GL(1)
In this talk, I will explain how to use the Fourier expansion
for the nonholomorphic Eisenstein series to show that
the zeta function is nonvanishing on the 1line. 

02/17 4:00pm 
Bloc605ax 
Erik Davis Texas A&M University 
An Elementary Proof of Bertrand's Postulate
In 1845, Bertrand conjectured that for every natural number n beyond 1, there exists a prime between n and 2n. Bertrand was not able to prove this conjecture but had verified the truth of the statement for each n up to 3,000,000. In 1850, Chebyshev proved the result using techniques of complex analysis and a shorter analytic proof was later given by Ramanujan. Despite the simple statement of the theorem, the mathematical community was not successful in finding an elementary proof of the result until 1932, when an 18 year old Paul Erdős deduced the result by observing a few properties of the central binomial. In this talk, I will provide the elementary proof first given by Paul Erdős. 

02/24 4:00pm 
Bloc605ax 
WeiCheng Huang Texas A&M University 
Nonvanishing property of Multiple Zeta Values in function fields
Multiple Zeta Values (MZVs) are interesting special values for number theorists. In this talk, I will give an introduction to MZVs in function fields and follow Thakur's method (2009) to prove that they are nonvanishing. 

03/02 4:00pm 
Bloc605ax 
Bradford Garcia Texas A&M University 
The Adeles over Q
In this talk, I plan to introduce the adeles over Q by first
discussing the field of padic numbers and how we can define padic
integration. Following this, we will build up some familiar machinery
such as the Fourier transform and the Poisson summation formula, but in
the language of adeles. Time permitting, we will then consider
automorphic forms for the general linear group of degree 1 over the
adeles. 