On a Diophantine Inequality with Reciprocals

被引:5
作者
Korolev, M. A. [1 ]
机构
[1] Russian Acad Sci, Steklov Math Inst, Ul Gubkina 8, Moscow 119991, Russia
基金
俄罗斯科学基金会;
关键词
KLOOSTERMAN SUMS; PRIME;
D O I
10.1134/S0081543817080090
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A sharpened lower bound is obtained for the number of solutions to an inequality of the form alpha ae{(anI... + bn)/q} < beta, 1 ae n ae N, where q is a sufficiently large prime number, a and b are integers with (ab, q) = 1, nnI... ae 1 (mod q), and 0 ae alpha < beta ae1. The length N of the range of the variable n is of order q (epsilon), where epsilon > 0 is an arbitrarily small fixed number.
引用
收藏
页码:132 / 142
页数:11
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