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FRACTIONAL PARTS OF POLYNOMIALS OVER THE PRIMES. II
Author(s) -
Baker Roger
Publication year - 2018
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579318000244
Subject(s) - mathematics , sharpening , irrational number , modulo , distribution (mathematics) , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , geometry , computer science , computer vision
Let | ⋯ | denote distance from the integers. Let α , β , γ be real numbers with α irrational. We show that the inequality‖ α p 2 + β p + γ ‖ < p − 3 / 17 + εhas infinitely many solutions in primes p , sharpening a result due to Harman [On the distribution of α p modulo one II. Proc. Lond. Math. Soc. (3) 72 (1996), 241–260] in the case β = 0 and Baker [Fractional parts of polynomials over the primes. Mathematika 63 (2017), 715–733] in the general case.