On a Binary Diophantine Inequality Involving Prime Numbers期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On a Binary Diophantine Inequality Involving Prime Numbers

Authors:	M. B. S. Laporta

Affiliation:	(1) Dipartimento di Matematica e Appl. "R. Caccioppoli", Complesso Universitario di Monte S. Angelo, Via Cinthia, 80126 Napoli, Italy

Abstract:	Let 1 < c < 15/14 and N a sufficiently large real number. In this paper we prove that, for all (N, 2N A with $left\| A right\| = Oleft( {N expleft( { - frac{1}{3}left( {frac{L}{c}} right)^{1/5} } right)} right)$ , the inequality $left\| {p_1 ^c + p_2 ^c - eta } right\| < eta ^{1 - frac{{15}}{{14c}}} L^8$ has solutions in primes $p_1 ,p_2 underline{underline < } N^{frac{1}{c}}$ .

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