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Seminar

Analytic Number Theory Seminar: Levels of distribution for prehomogeneous vector spaces February 21, 2017 (02:00 PM PST - 03:00 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Frank Thorne (University of South Carolina)
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A "level of distribution" is, in essence, a bound on the cumulative error terms made in counting subsequences of some arithmetic sequence of interest. These are often an important tool in analytic number theory arguments, and I will begin with an overview of some interesting applications (due mostly to people other than me!) involving prehomogeneous vector spaces and their parametrizations.



I will then outline our* program to prove level of distribution statements which are as quantitatively strong as possible, and in as much generality as possible. The first part is an evaluation of some associated exponential sums over finite fields, where we observe better than square root cancellation. The second part relies on the geometry and orbit structure of our vector spaces to put these exponential sum estimates to good use.



*: Joint work with Takashi Taniguchi

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