Number Theory Seminar
Nathan Jones
University of Illinois at Chicago
A local-global principle for power maps
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.
Tuesday September 30, 2014 at 11:00 AM in SEO 427