## K Ramachandra - On a method of Davenport and Heilbronn I.

hrj:136 - Hardy-Ramanujan Journal, January 1, 1998, Volume 21 - 1998 - https://doi.org/10.46298/hrj.1998.136
On a method of Davenport and Heilbronn I.

Authors: K Ramachandra

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 $p_j$.

Volume: Volume 21 - 1998
Published on: January 1, 1998
Imported on: March 3, 2015
Keywords: Davenport-Heilbronn fundamental method, basic, intermediary and supplementary intervals,[MATH] Mathematics [math]