On Artin's conjecture for primitive roots

• Main Author: Pappalardi, Francesco
• Other Authors: Murty, Ram (advisor)
• Format: Others
• Language: en
• Published: McGill University 1993
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41128

Various generalizations of the Artin's Conjecture for primitive roots are considered. It is proven that for at least half of the primes p, the first log p primes generate a primitive root. A uniform version of the Chebotarev Density Theorem for the field ${ cal Q}( zeta sb{l},2 sp{1/l})$ valid for the range $l < { rm log} x$ is proven. A uniform asymptotic formula for the number of primes up to x for which there exists a primitive root less than s is established. Lower bounds for the exponent of the class group of imaginary quadratic fields valid for density one sets of discriminants are determined.