A ternary Diophantine inequality over primes
Volume 162 / 2014
Acta Arithmetica 162 (2014), 159-196
MSC: Primary 11N36; Secondary 11L20, 11P55.
DOI: 10.4064/aa162-2-3
Abstract
Let $1< c< 10/9$. For large real numbers $R>0$, and a small constant $\eta >0$, the inequality $$ | p_1^c+p_2^c+p_3^c - R| < R^{-\eta } $$ holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].
