Displaying similar documents to “Corrigendum to the paper 'A problem of Erdös concerning power residue sums' (Acta Arithmetica 12 (1968), pp. 131-149)”

Artin's primitive root conjecture for quadratic fields

Hans Roskam (2002)

Journal de théorie des nombres de Bordeaux

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Fix an element α in a quadratic field K . Define S as the set of rational primes p , for which α has maximal order modulo p . Under the assumption of the generalized Riemann hypothesis, we show that S has a density. Moreover, we give necessary and sufficient conditions for the density of S to be positive.

The correction factor in Artin's primitive root conjecture

Peter Stevenhagen (2003)

Journal de théorie des nombres de Bordeaux

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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...

Stark's conjecture in multi-quadratic extensions, revisited

David S. Dummit, Jonathan W. Sands, Brett Tangedal (2003)

Journal de théorie des nombres de Bordeaux

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Stark’s conjectures connect special units in number fields with special values of L -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent 2 . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.