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Seminar

Analytic Number Theory Graduate Student Seminar April 04, 2017 (04:00 PM PDT - 05:00 PM PDT)
Parent Program:
Location: MSRI: Baker Board Room
Speaker(s) Oleksiy Klurman (Université de Montréal), Raphael Steiner (University of Bristol)
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4.00pm:

​Raphael Steiner​

​Title: ​On a twisted version of the Linnik-Selberg conjecture

Abstract: We discuss cancellation in sums of Kloosterman sums against a new kind of twist: \sum_{q \le Q}​q^{-1}​S(m,n,q)e_q(2\sqrt{mn}\alpha). By making use of Kuznetsov's trace formula we are able to prove bounds as strong as the ones given by Sarnak and Tsimerman for \alpha=0, provided that |\alpha|\le​q​ 1 - \delta. Comparable bounds for larger​ ​\alpha continue to hold.

 

4.30pm:

​Oleiksy ​Klurman

Title: Correlations of multiplicative functions

Abstract: ​ ​We discuss asymptotic formulas for correlations \sum_{n\le x} f_1(P_1(n))\dots f_k(P_k(n)), where f_1,\dots,f_k are so-called  "pretentious" multiplicative functions and P_i(x)\in\mathbb{Z}[x]. Combining with the breakthrough works of Matomaki, Radziwill and Tao we apply these formulas to resolve/make partial progress towards some open problems concerning multiplicative functions.


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