Seminar

A century ago, motivated by the problem of bounding the least quadratic nonresidue, Polya and Vinogradov proved a bound on character sums which is very strong for long sums, but useless for estimating short character sums. Forty years later, Burgess proved a bound which is effective for short(-ish) character sums, but useless for long sums. In this talk I will describe relations between these two bounds, including recent work -- joint with Elijah Fromm (Williams College '17) -- showing that in special cases, progress on either bound implies progress on the other.