Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Hasse Polynomials of L-functions of Certain Exponential Sums

Chao Chen
Friday, October 25, 2019
5:00 pm - 5:50 pm
RH 440R

Talk Abstract:

Estimating exponential sums is a classical problem in number theory. This problem can be reduced to evaluate the reciprocal roots and zeros of the associated L-functions. In this talk, we will focus on certain exponential sums constructed by Laurent polynomials over finite field of characteristic p and study the variation of p-adic absolute values. Newton polygon is the main tool to estimate p-adic valuations. Adolphson and Sperber proved that the Newton polygon of L-function of a non-degenerate Laurent polynomial has a topological lower bound Hodge polygon. We will discuss when Newton polygon reaches Hodge polygon. Hasse polynomials are constructed to determine the coincidence of Newton polygons and Hodge polygons. We compute the higher slope Hasse polynomials and study the irreducibility of these polynomials.

About the Speaker:

Chao is a 4th year PhD student interested in number theory. In her spare time, she enjoys watching anime.

Refreshments:

Pizza will be served after the talk.