Hardy Ramanujan Journal |

Let $\lambda_1, \lambda_2, \lambda_3$ be nonzero reals with $\lambda_1/\lambda_3$ negative irrational. Let $\varphi_j(u)\,(1\leq j\leq3)$ be smooth functions with derivatives $<\!\!\!< u^{-1}(\log u)^C\,(u\geq3)$. We prove in this paper that the inequality $\vert\sum_{j=1}^3\lambda_j(p_j+\varphi_j(p))\vert < \exp(-(\log(p_1p_2p_3))^{1/2})$ holds for infinitely many triplets of primes $p_j$.

Source : oai:HAL:hal-01109319v1

Volume: Volume 21

Published on: January 1, 1998

Submitted on: March 3, 2015

Keywords: Davenport-Heilbronn fundamental method, basic, intermediary and supplementary intervals,[MATH] Mathematics [math]

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