## Columbia Mathematics Department Colloquium

*``Values of zeta functions at negative integers and the
dimensions*

*of** spaces of modular forms"*

### by

### Benedict Gross

### Harvard
University

Abstract:

Euler introduced the zeta function into number theory, and proved a number of
beautiful results

on the values of the zeta
function at negative integers, using clever techniques to sum divergent series.

I will review the modern
theory, which uses analytic continuation to define these values, and relate

the values to the dimensions of
certain spaces of modular forms.

**April 15th, Wednesday, 5:00-6:00 pm**

**Mathematics 312**

**Tea will be served at 4:30pm**