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Seminar

Analytic Number Theory Seminar: The long and the short of character sums April 13, 2017 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Leo Goldmakher (Williams College)
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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.

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