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A ternary Diophantine inequality over primes

Roger Baker, Andreas Weingartner (2014)

Acta Arithmetica

Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality | p c + p c + p c - R | < R - η holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].

Additive properties of dense subsets of sifted sequences

Olivier Ramaré, Imre Z. Ruzsa (2001)

Journal de théorie des nombres de Bordeaux

We examine additive properties of dense subsets of sifted sequences, and in particular prove under very general assumptions that such a sequence is an additive asymptotic basis whose order is very well controlled.

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