MATH Seminar

Title: Topics in analytic number theory
Defense: Dissertation
Speaker: Robert Lemke Oliver of Emory University
Contact: Robert Lemke Oliver, rlemkeo@emory.edu
Date: 2013-04-04 at 2:30PM
Venue: MSC E408
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Abstract: In this thesis, the author proves results using the circle method, sieve theory and the distribution of primes, character sums, modular forms and Maass forms, and the Granville-Soundararajan theory of pretentiousness. In particular, he proves theorems about partitions and $q$-series, almost-prime values of polynomials, Gauss sums, modular forms, quadratic forms, and multiplicative functions exhibiting extreme cancellation. This includes a proof of the Alder-Andrews conjecture, generalizations of theorems of Iwaniec and Ono and Soundararajan, and answers to questions of Zagier and Serre, as well as questions of the author in the Granville-Soundararajan theory of pretentiousness.\\ \\ The talk will focus on three topics: Gauss sums over finite fields, eta-quotients and theta functions, and the pretentious view of analytic number theory.