Type: Seminar

Distribution: World

Expiry: 24 Sep 2013

Auth: zhangou@como.maths.usyd.edu.au

Speaker: Bryce Kerr (Macquarie) Time: Thursday, Sept. 5, 12NOON--1PM Room: Carslaw 707A Lunch: after the talk, at Law Annex Cafe. ---------------------------------------------- Title: Character Sums Over Shifted Primes Abstract: For integer $q$, let $\chi$ be a primitive character of the multiplicative group $\left(\mathbb{Z}/q\mathbb{Z}\right)^{*}$. For any integer $a$ coprime to $q$, we consider bounding the sums $\sum_{p\le N}\chi(p+a)$ where the above sum is over all prime numbers less than $N$. We show cancellation in such sum occurs in the range $N\ge q^{5/6+\varepsilon}$ which improves a result of Friedlander, Gong and Shparlinski. ---------------------------------------------- Seminar website: http://www.maths.usyd.edu.au/u/SemConf/Geometry/