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| on the distribution of pseudorandom numbers and vectors derived from euler-fermat quotients | |
| Chen Zhixiong; Winterhof Arne | |
| 2012 | |
| Source | INTERNATIONAL JOURNAL OF NUMBER THEORY
 |
| ISSN | 1793-0421 |
| Volume | 8Issue:3Pages:631-641 |
| English Abstract | 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.; 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. |
| Indexed Type | SCI |
| Keyword | PseudorAndom Numbers And Vectors Euler Quotients Fermat Quotients Exponential Sums Discrepancy |
| Department | Chen Zhixiong Putian Univ Dept Math Putian 351100 Fujian Peoples R China. Chen Zhixiong Chinese Acad Sci Inst Software State Key Lab Informat Secur Beijing 100049 Peoples R China. Winterhof Arne Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria. |
| Subject | Mathematics |
| Sponsorship | Austrian Academy of Sciences; National Natural Science Foundation of China 61170246; Fujian Province University of China JK2010047; State Key Laboratory of Information Security (Chinese Academy of Sciences) 01-01-1 |
| Language | 英语 |
| WOS ID | WOS:000302020300005 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15084 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation GB/T 7714 | Chen Zhixiong,Winterhof Arne. on the distribution of pseudorandom numbers and vectors derived from euler-fermat quotients[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY,2012,8(3):631-641. |
| APA | Chen Zhixiong,&Winterhof Arne.(2012).on the distribution of pseudorandom numbers and vectors derived from euler-fermat quotients.INTERNATIONAL JOURNAL OF NUMBER THEORY,8(3),631-641. |
| MLA | Chen Zhixiong,et al."on the distribution of pseudorandom numbers and vectors derived from euler-fermat quotients".INTERNATIONAL JOURNAL OF NUMBER THEORY 8.3(2012):631-641. |
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