Caltech Logo

Joint Berkeley-Caltech-Stanford Number Theory Seminar

Monday, November 16, 2020
12:30pm to 2:00pm
Add to Cal
Online Event
An asymptotic version of the prime power conjecture for perfect difference sets
Sarah Peluse, Department of Mathematics, Princeton University/IAS,

A subset D of a finite cyclic group Z/mZ is called a "perfect difference set" if every nonzero element of Z/mZ can be written uniquely as the difference of two elements of D. If such a set exists, then a simple counting argument shows that m=n^2+n+1 for some nonnegative integer n. Singer constructed examples of perfect difference sets in Z/(n^2+n+1)Z whenever n is a prime power, and it is an old conjecture that these are the only such n for which a perfect difference set exists. In this talk, I will discuss a proof of an asymptotic version of this conjecture: the number of n less than N for which Z/(n^2+n+1)Z contains a perfect difference set is ~N/log(N).

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.