##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Audrey Terras

#### UCSD

## A new kind of zeta function: When number theory meets graph theory

##### Abstract:

I will present an introduction to zeta and L-functions of graphs by comparison with the zeta and L-functions of number theory. Basic properties will be discussed, including: the Ihara formula saying that the zeta function is the reciprocal of a polynomial. I will then explore graph analogs of the Riemann hypothesis, the prime number theorem, Chebotarev's density theorem, zero (pole) spacings, and connections with expander graphs and quantum chaos. References include my joint papers with Harold Stark in Advances in Mathematics. There is also a book I am writing on my website: http://math.ucsd.edu/\%7Eaterras/newbook.pdf

### October 11, 2007

### 2:00 PM

### AP&M 7321

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