ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER–FERMAT QUOTIENTS
ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER–FERMAT QUOTIENTS
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DOI：
10.1142/s1793042112500352
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发表时间：
2012-04
影响因子：
0.7
通讯作者：
Zhixiong Chen;Arne Winterhof
中科院分区：
文献类型：
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作者：
Zhixiong Chen;Arne Winterhof
我们研究了以复合m为模的连续欧拉-费马商的s维向量的分布。更准确地说，我们分别基于著名的Burgess界和以m为模的多项式的0个数的界证明了s = 1和s > 1的两个不同的差异界。所得结果推广了一些已知的费马商与Ostafe和Shparlinski的模a素的界。然而，复合模量的情况带来了一些有趣的转折。
We study the distribution of s-dimensional vectors of consecutive Euler–Fermat quotients modulo a composite m. More precisely, we prove two different discrepancy bounds for s = 1 and s > 1 based on the celebrated Burgess bound and on bounds on the number of zeros of a polynomial modulo m, respectively. The results extend some known bounds for Fermat quotients modulo a prime of Ostafe and Shparlinski. However, the case of composite modulus brings some interesting twists.