A generalization of Lehmer's functions

H. Williams

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In 1927, E. Artin proposed a conjectural density for the set of primes $p$ for which a given integer $g$ is a primitive root modulo $p$ . After computer calculations in 1957 by D. H. and E. Lehmer showed unexpected deviations, Artin introduced a correction factor to explain these discrepancies. The modified conjecture was proved by Hooley in 1967 under assumption of the generalized Riemann hypothesis. This paper discusses two recent developments with respect to the correction factor. The first...

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