RESEARCH ARTICLE

Values of binary linear forms at prime arguments

  • Yuchao WANG
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  • Department of Mathematics, Shanghai University, Shanghai 200444, China

Received date: 11 Jan 2015

Accepted date: 21 Feb 2015

Published date: 12 Oct 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence V and δ>0, let E(V, X, δ) denote the number of υV with υX for which the inequality

|λ1p1+λ2ρ2υ|<υδ

has no solution in primes p1, p2. It is shown that for any ε>0,we have E(V, X, δ) «max(X35+2δ+ε,X23+43δ+ε).

Cite this article

Yuchao WANG . Values of binary linear forms at prime arguments[J]. Frontiers of Mathematics in China, 2015 , 10(6) : 1449 -1459 . DOI: 10.1007/s11464-015-0461-3

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