COUNTING POINTS MODULO p FOR SOME FINITELY GENERATED SUBGROUPS OF ALGEBRAIC GROUPS

@inproceedings{Matthews1982COUNTINGPM,
  title={COUNTING POINTS MODULO p FOR SOME FINITELY GENERATED SUBGROUPS OF ALGEBRAIC GROUPS},
  author={Charles R. Matthews},
  year={1982}
}
We begin by explaining the basic idea of this paper in a simple case. We write n p for the order of 2 modulo the prime p, so that n p is the number of powers of 2 which are distinct mod p. We have the elementary bounds logp <£ n p ^ p-1. The conjecture of E. Artin on primitive roots asserts that the upper bound is attained for a set of primes with positive density (see Hooley [2] for a discussion of conditional proofs in this case). The lower bound may be improved to P * " < n p for almost all… CONTINUE READING