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Analytic Number Theory Graduate Student Seminar March 21, 2017 (04:00 PM PDT - 05:00 PM PDT)
Parent Program:
Location: MSRI: Baker Board Room
Speaker(s) David Lowry-Duda (Brown University), Corentin Perret-Gentil-dit-Maillard (ETH Zürich)
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4.00pm: ​Corentin Perret-Gentil

​Title: ​Exponential sums and the large sieve

​Abstract:​  We discuss the use of the large sieve for Frobenius in compatible systems along with finite monodromy groups to study the distribution of families of exponential sums in the cyclotomic integers.


4.30pm: David Lowry-Duda

Title: Using Modular Forms to Count Lattice Points on Hyperboloids

Abstract: We describe how to use modular forms to get accurate asymptotics for the number of integer lattice points on one-sheeted hyperboloids such as X^2 + Y^2 = Z^2 + 1. We will frame this in the general framework of how to use and understand shifted convolution sums coming from modular forms.

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