Geodesic
Diophantine approximation by prime numbers of a special form
Serdica Mathematical Journal, Tome 47 (2022) no. 3, pp. 255-272.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

We show that whenever \(\delta>0\), \(\eta\) are reals and constants \(\lambda _i\) subject to certain assumptions, there are infinitely many prime triples \(p_1, p_2, p_3\) satisfying the inequality \(|\lambda _1p_1 + \lambda _2p_2 + \lambda _3p_3+\eta| < (\max p_j)^{-1/18+\delta }\) and such that, for each \(i\in\{1,2,3\}\), \(p_i+2\) has at most 7 prime factors. The proof uses Davenport–Heilbronn adaption of the circle method together with a vector sieve method.
Keywords: Rosser's weights, vector sieve, circle method, almost primes, diophantine inequality, 11D75, 11N36, 11P32 
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Todorova, Tatiana. Diophantine approximation by prime numbers of a special form. Serdica Mathematical Journal, Tome 47 (2022) no. 3, pp. 255-272. http://geodesic.mathdoc.fr/item/SMJ2_2022_47_3_a4/