In the exact formula for the partition function, there is a curious Kloosterman sum. The convergence for the infinite series for p(n) relies upon a bound for this Kloosterman sum. This Kloosterman sum is related to the multiplier system of a weight 1/2 modular form, and we can in general define the Kloosterman sum for a given multiplier system. In this talk, we will focus on the Kloosterman sums of half-integral weight for the Weil representation attached to an even lattice, and we will show that the Weil bound holds for these sums. This talk will give an introduction to modular forms, the Weil representation, and Kloosterman sums and is aimed toward a general audience interested in number theory.

Talk by Amy Woodall.