Christopher Towse's Abstract

 

Claremont Mathematics Weekend

 

Sponsored by Claremont Colleges

 

January 30 - 31, 2016

 

Speaker: Christopher Towse
Title: Some Basics of Analytic Number Theory: Functions that encode Arithmetic Data
Abstract:

Many fundamental properties of integers can be described in terms of arithmetic functions. (Is a number a square? Is a number a prime? How many divisors does a number have?) Arithmetic functions can be used as a way to describe many fundamental properties of integers: Is a number a square? Is a number a prime? How many divisors does a number have? We can encode this information using types of generating functions. In this talk we will see how to encode and decode number theoretic information using Dirichlet series and their Euler products. We will look at the resulting functions, including the famous Riemann zeta function, which has a million dollar prize attached to it.