ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER–FERMAT QUOTIENTS-Reference-Cited by-同舟云学术

ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER–FERMAT QUOTIENTS

Published:2012-04-07 Issue:03 Volume:08 Page:631-641
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

CHEN ZHIXIONG¹²,WINTERHOF ARNE³

Affiliation:

1. Department of Mathematics, Putian University, Putian, Fujian 351100, P. R. China

2. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100049, P. R. China

3. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz, Austria

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.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042112500352

Reference25 articles.

1. Fermat Quotients for Composite Moduli

2. Boolean functions derived from Fermat quotients

3. Trigonometric approximation and uniform distribution modulo one

4. Digital Nets and Sequences

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