Nathan Jones : A local-global principle for power maps

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

At

April 23, 2013, 1:15 p.m.

In

SEO 636

Abstract

Let $f$ be a function from the set of natural numbers to itself. We call $f$ a global power map if $f(n) = n^k$ for some non-negative integer exponent $k$. For a set $S$ of prime numbers, we call f {a local power map at $S$ if for each prime $p$ in $S$, $f$ induces a well-defined group homomorphism on the multiplicative group $(Z/pZ)^*$. In this talk, I will motivate the conjecture that if $f$ is a local power map at an infinite set $S$ of primes, then $f$ must be a global power map. I will also discuss some progress towards this conjecture.