The Euclidean algorithm and primitive roots

12/08/2009 - 12:15pm
12/08/2009 - 1:10pm
Kate Petersen (Florida State University)

Artin conjectured that if b is an integer other than -1 or a square, then b is a primitive root modulo infinitely many primes. Although still unproven, this conjecture is known to be true under the assumption of the generalized Riemann hypothesis. I will discuss the history and some motivation behind studying this conjecture, and survey some known results. I will introduce a generalization of the primitive root conjecture to number fields and discuss some applications including a direct connection to the determination of number rings with a Euclidean Algorithm. This is joint work with Ram Murty.

Millikan 208 (Pomona College)