Nathan Jones : A local-global principle for power maps

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

Sept. 30, 2014, 11 a.m.

In

SEO 427

Abstract

Let f be a function from the set of integers into itself. We call f a global power map if there exists a non-negative integer k so that f(x) = x^k for every integer x. We call f a local power map at the prime number p if f induces a well-defined group homomorphism on the multiplicative group of integers modulo p. It has been conjectured that, if f is a local power map at infinitely many primes p, then f is a global power map. In this talk, I will discuss a theorem implying that, if f is a local power map at all primes p in a set with positive upper density relative to the set of all primes, then f must be a global power map.

The seminar will end at 12:30. Snacks will follow.