Geodesic
DIOPHANTINE APPROXIMATION BY PRIMES
Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 87-106

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DOI

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.
DOI : 10.1017/S0017089509990176
Mots-clés : 11D75, 11N36, 11P32 
MATOMÄKI, KAISA. DIOPHANTINE APPROXIMATION BY PRIMES. Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 87-106. doi: 10.1017/S0017089509990176
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     title = {DIOPHANTINE {APPROXIMATION} {BY} {PRIMES}},
     journal = {Glasgow mathematical journal},
     pages = {87--106},
     year = {2010},
     volume = {52},
     number = {1},
     doi = {10.1017/S0017089509990176},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990176/}
}
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