On a method of Davenport and Heilbronn I.
Ramachandra, K
HAL, hal-01109319 / Harvested from HAL
Text on HAL
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 $p_j$.
Publié le : 1998-07-04
Classification:  Davenport-Heilbronn fundamental method,  basic,  intermediary and supplementary intervals,  [MATH]Mathematics [math] 
@article{hal-01109319,
     author = {Ramachandra, K},
     title = {On a method of Davenport and Heilbronn I.},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01109319}
}

Ramachandra, K. On a method of Davenport and Heilbronn I.. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-01109319/