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The values of ternary quadratic forms at prime arguments

Published online by Cambridge University Press:  26 February 2010

R. J. Cook  and
A. Fox
R. J. Cook
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield RoadSheffield S3 7RHCurrent address: Stoneygate, Bessie Lane, Bradweli, Hope Valley S33 9HZ
A. Fox
Affiliation:
2 Clarence Road, Monk Bretton, Barnsley, South Yorkshire S71 2NL.
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Extract

Montgomery and Vaughan [12] have shown that the exceptional set in Goldbach's problem

satisfies

for some Δ>0. Li [10,11] has shown that we may take Δ = 0·079 and Δ = 0·086. If the Riemann Hypothesis is true for all Dirichlet L-functions then (1) holds for any Δ<½. This is a classical result due to Hardy and Littlewood [7].

Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 137 - 149
Copyright
Copyright © University College London 2001

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