Number Theory Seminar
Nathan Jones
university of Mississippi and UIC
A local-global principle for power maps
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.
Tuesday April 23, 2013 at 1:15 PM in SEO 636