Title | DIOPHANTINE APPROXIMATION BY PRIME NUMBERS OF A SPECIAL FORM |
Publication Type | Journal Article |
Year of Publication | 2015 |
Authors | Dimitrov S., Todorova T. |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 102 |
Pagination | 71-90 |
ISSN | 0205-0808 |
Keywords | almost primes, circle method, diophantine inequality, Rosser’s weights, vector sieve |
Abstract | We show that for $B > 1$ and for some constants $\lambda_i, i = 1, 2, 3$ subject to certain assumptions, there are infinitely many prime triples $p_1, p_2, p_3$ satisfying the inequality $\mid\lambda_1p_1 + \lambda_2p_2 + \lambda_3p_3 + \eta\mid < [log(max\,p_j )]^{-B}$ and such that $p_1 + 2, \, p_2 + 2\, and \, p_3 + 2$ have no more than 8 prime factors. The proof uses Davenport - Heilbronn adaption of the circle method together with a vector sieve method. |
2000 MSC | 11D75, 11N36, 11P32 |
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102-071-090.pdf | 221.75 KB |