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Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1190551
Description: In this paper we study the mapping properties of the averaging operator over a variety given by a system of homogeneous equations over a finite field. We obtain optimal results on the averaging proble ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195678
Description: In this paper, we give a general explicit form of Cassels’ p-adic embedding theorem for number fields. We also give its reûned form in the case of cyclotomic fields. As a byproduct, given an irreducib ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332341
Description: We present several general results that show how algebraic dynamical systems with a slow degree growth and also rational automorphisms can be used to construct stronger pseudorandom number generators. ... More
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Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332353
Description: We show that the pseudo-random number function, introduced by M. Naor and O. Reingold (FOCS, 1997), possesses one more attractive anduseful property. Namely, it is proved that for almost all values of ... More
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Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/305780
Description: Circulant graphs are regular graphs based on Cayley graphs defined on the Abelian group Zn. They are popular network topologies that arise in distributed computing. Using number theoretical tools, we ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/278997
Description: We obtain analogues of several recent bounds on the number of solutions of polynomial congruences modulo a prime with variables in short intervals in the case of polynomial equations in high degree ex ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: book
Identifier: http://hdl.handle.net/1959.14/271071
Description: Collects contributions based on the proceedings of "International Number Theory Conference in Memory of Alf van der Poorten." These proceedings will presents high quality research articles and compreh ... More
Date: 2012
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/195847
Description: We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/200223
Description: Using a recent result on the sum-product problem, we estimate the number of elements γ in a prime finite field such that both γ and γ+γ⁻¹ are of small order. Correction to this article published in Bu ... More
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Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: reference entry
Identifier: http://hdl.handle.net/1959.14/159913
Description: 5 page(s)
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/119092
Description: Let E be an ordinary elliptic curve over a finite field Fq of q elements. We improve a bound on bilinear additive character sums over points on E, and obtain its analogue for bilinear multiplicative c ... More
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Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129331
Description: We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of von zur Gathen and Shparlinski.
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130393
Description: 6 page(s)
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/320300
Description: 10 page(s)
Reviewed: Reviewed
Date: 2008
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/320415
Description: 7 page(s)
Reviewed: Reviewed