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On extending Artin's conjecture to composite moduli
Published online by Cambridge University Press: 26 February 2010
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It is well known that, if p is prime, the multiplicative group (ℤ/pℤ)* of reduced residues is cyclic. A generator is called a primitive root; there are φ(p − 1) of them, where φ is Euler's function. Thus, (φ(p − 1)/(p−1) is the proportion of primitive roots modulo p in (ℤ/pℤ)*. Elliott has proved that φp − 1)/(p − 1) has a limiting distribution function [2], in the sense that
exists for all real numbers u.
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- Copyright © University College London 1999
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