ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11R45, 11A07, 11N69 Moree, Pieter, Max-Planck-Institut, Bonn, Germany Distribution of primes having a prescribed primitive root over residue classes Let g be an integer and p a prime. The integer g is said to be a primitive root mod p if the smallest positive integer k such that g^{k} ≡ 1(mod p) equals p − 1. Let P_{g} denote the set of primes p such that g is a primitive root mod p. Let d ≥ 1 be an integer. All pairs (g, d) are determined such that every primitive residue class mod d gets ‘an equal share’ asymptotically from P_{g}. This research is motivated by a conjecture of Rodier [2], which turns out to be false. References [1] P. Moree, Uniform distribution of primes having a prescribed rational primitve root, MPI-preprint 98-23. (Available on the web under http://www.mpim-bonn.mpg.de/ html/preprints.html). [2] P. Moree, On a conjecture of Rodier on primitve roots, Abh. Math. Sem. Univ. Hamburg 67 (1997), 165-171.