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The Distribution of Primitive Roots

Published online by Cambridge University Press:  20 November 2018

P. D. T. A. Elliott
P. D. T. A. Elliott*
Affiliation:
University of Nottingham, Nottingham, England
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Notation,p and q are generic symbols for prime numbers. N(H, p) denotes the number of primes q, not exceeding Hy which are primitive roots (mod p).

g(p) denotes the least positive primitive root (mod p).

g*(p) is the least prime primitive root (mod p).

v(m) denotes the number of distinct prime divisors of the integer m.

τk(m) is the number of ways of representing the integer m as the product of k integers, order being important.

π(x, k, r) is the number of primes p, not exceeding x, which satisfy p ≡ r(mod k); while π(x) denotes the total number of p ≦ x.

logm x denotes the mth iterated logarithmic function which is defined, when possible, by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 822 - 841
Copyright
Copyright © Canadian Mathematical Society 1969

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