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Abstract: this paper is to provide an improvement on a recent result [9] of the second author regarding the solvability of inequality (1.1) for s = 2. In [9] it is proved that, for almost all y # [N, 2N) (i.e., the Lebesgue measure of the set of the exceptions is o(N )), the following inequality has solutions in primes p 1 , p 2 : # # p c 1 + p c 2 - y # # < # (1.2) where # = N 1-15/(14c) log C N with 1 < c < 15/14 and for some positive constant C (and, in fact, a more careful... (Update)
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BibTeX entry: (Update)
@misc{ kumchev-binary,
author = "A. Kumchev and M. B. S. Laporta",
title = "On A Binary Diophantine Inequality Involving Prime Powers",
url = "citeseer.ist.psu.edu/498707.html" }
Citations (may not include all citations):51 London Math (context) - Harman, distribution et al. - 1983
29 Ten Lectures on the Interface Between Analytic Number Theory.. (context) - Montgomery - 1994
2 Diophantine approximation by cubes of primes and an almost p.. (context) - Brudern, Kumchev
2 a diophantine inequality involving prime numbers (context) - Cai - 1996
2 modulo one II (context) - Harman, distribution - 1996
2 Additive Theory of Prime Numbers (context) - Hua - 1965
2 a diophantine inequality involving prime numbers (context) - Tolev - 1992
1 the Piatetski-Shapiro--Vinogradov theorem (context) - Jia - 1995
1 Multiple exponential sums with monomials and their applicati.. (context) - Sargos, Wu - 2000
1 A diophantine inequality involving prime powers (context) - Kumchev - 1999
1 a variant of Waring-Goldbach's problem (context) - Piatetski-Shapiro - 1952
1 an equation with prime numbers (context) - Kumchev, Nedeva - 1998
1 in Russian). Department of Mathematics University of South C.. (context) - Vinogradov, an et al. - 1937
1 a binary diophantine inequality involving prime numbers (context) - Laporta - 1999
1 the number of abelian groups of a given order (context) - Liu - 1991
Documents on the same site (http://www.math.toronto.edu/kumchev/):
Diophantine Approximation By Cubes Of Primes And An Almost.. - Brüdern, Kumchev (2001) (Correct)
The Distribution Of Prime Ideals Of Imaginary Quadratic Fields - Harman, Kumchev, Lewis (Correct)
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