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DIOPHANTINE APPROXIMATION BY PRIMES

Published online by Cambridge University Press:  31 July 2009

KAISA MATOMÄKI
KAISA MATOMÄKI*
Affiliation:
Department of Mathematics, University of Turku, 20014 Turku, Finland e-mail: [email protected]
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Abstract

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We show that whenever δ > 0 and constants λi satisfy some necessary conditions, there are infinitely many prime triples p1, p2, p3 satisfying the inequality |λ0 + λ1p1 + λ2p2 + λ3p3| < (max pj)−2/9+δ. The proof uses Davenport–Heilbronn adaption of the circle method together with a vector sieve method.

Keywords

11D7511N3611P32
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 87 - 106
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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