Seminars & Colloquia Calendar
An asymptotic version of the prime power conjecture for perfect difference sets
Sarah Peluse (Princeton University)
Date & time: Tuesday, 02 February 2021 at 2:00PM - 3:00PM
Abstract: 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).
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