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Copyright © 2011 Claremont Center for the Mathematical Sciences

**Claremont Mathematics Weekend**

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*Sponsored by Claremont Colleges*

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**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.