DIOPHANTINE APPROXIMATION BY PRIME NUMBERS OF A SPECIAL FORM

TitleDIOPHANTINE APPROXIMATION BY PRIME NUMBERS OF A SPECIAL FORM
Publication TypeJournal Article
Year of Publication2015
AuthorsDimitrov S., Todorova T.
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume102
Pagination71-90
ISSN0205-0808
Keywordsalmost 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

AttachmentSize
PDF icon 102-071-090.pdf221.75 KB