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2010 EXPONENTIAL SUMS FOR NONLINEAR RECURRING SEQUENCES IN RESIDUE RINGS
Edwin El-Mahassni
Author Affiliations +
Albanian J. Math. 4(1): 3-13 (2010). DOI: 10.51286/albjm/1280193570

Abstract

We prove some new bounds on exponential sums for nonlinear recurring sequences over residue rings. In addition, we also show similar novel results when the modulus is almost squarefree, thereby improving the results in El-Mahassni, Shparlinski, and Winterhof [11] and El-Mahassni and Winterhof [13] This is done by using a technique employed by Niederreiter and Winterhof [26] and through the generalisation of a Lemma found in [11] and [13]. Lastly, applications to the distribution of nonlinear congruential pseudorandom numbers are also given.

Funding Statement

The author is very grateful to Igor Shparlinski for helpful comments and suggestions.

Citation

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Edwin El-Mahassni. "EXPONENTIAL SUMS FOR NONLINEAR RECURRING SEQUENCES IN RESIDUE RINGS." Albanian J. Math. 4 (1) 3 - 13, 2010. https://doi.org/10.51286/albjm/1280193570

Information

Published: 2010
First available in Project Euclid: 14 July 2023

Digital Object Identifier: 10.51286/albjm/1280193570

Subjects:
Primary: 11K45 , 11L07 , 65C10

Keywords: Discrepancy , exponential sums , nonlinear congruential method , pseudorandom numbers

Rights: Copyright © 2010 Research Institute of Science and Technology (RISAT)

Vol.4 • No. 1 • 2010
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