An application of exponential sum estimates

被引:0
|
作者
Yi, Y [1 ]
Zhang, WP [1 ]
机构
[1] Xian Jiaotong Univ, Res Ctr Basic Sci, Xian 710049, Peoples R China
关键词
exponential sum; trigonometric sums; asymptotic formula;
D O I
10.1007/s10114-004-0351-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let p be an odd prime and let delta be a fixed real number with 0 < delta < 2. For an integer a with 0 < a < p, denote by (a) over bar the unique integer between 0 and p satisfying as a (a) over bar equivalent to 1 (mod p). Further, let {x} denote the fractional part of x. We derive an asymptotic formula for the number of pairs of integers (a,b)with 1 less than or equal to a less than or equal to p-1,1 less than or equal to b less than or equal to p-1, \{a(k)/p}+{b(k)/p}-{a(-1)/p}-{b(-1)/p}\< delta.
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页码:851 / 858
页数:8
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