| Date: | February 3, 2020 |
| Time: | 4:00pm |
| Location: | Bloc 605AX |
| Speaker: | Jiakun Pan, Texas A&M University |
| Title: | Eisenstein series attached to cusps |
| Abstract: | 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. |
|
| Date: | February 10, 2020 |
| Time: | 4:00pm |
| Location: | Bloc605ax |
| Speaker: | Wei-Lun Tsai, Texas A&M University |
| Title: | Prime number theory--from GL(2) to GL(1) |
| Abstract: | In this talk, I will explain how to use the Fourier expansion
for the non-holomorphic Eisenstein series to show that
the zeta function is non-vanishing on the 1-line. |
|
| Date: | February 17, 2020 |
| Time: | 4:00pm |
| Location: | Bloc605ax |
| Speaker: | Erik Davis, Texas A&M University |
| Title: | An Elementary Proof of Bertrand's Postulate |
| Abstract: | 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. |
|
| Date: | February 24, 2020 |
| Time: | 4:00pm |
| Location: | Bloc605ax |
| Speaker: | Wei-Cheng Huang, Texas A&M University |
| Title: | Non-vanishing property of Multiple Zeta Values in function fields |
| Abstract: | 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 non-vanishing. |
|
| Date: | March 2, 2020 |
| Time: | 4:00pm |
| Location: | Bloc605ax |
| Speaker: | Bradford Garcia, Texas A&M University |
| Title: | The Adeles over Q |
| Abstract: | In this talk, I plan to introduce the adeles over Q by first
discussing the field of p-adic numbers and how we can define p-adic
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. |
|
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