Macquarie University, Sydney Macquarie University ResearchOnline

Showing items 196 - 210 of 373.

Add to Quick Collection   All 373 Results

Sort:
 Add All Items to Quick Collection
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/331872
Description: We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime p. In particular, we obtain nontrivial results about the number ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128917
Description: We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets ... More
Reviewed: Reviewed
Date: 2005
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1140322
Description: 6 page(s)
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130338
Description: We give explicit formulas for the number of distinct elliptic curves over a finite field (up to isomorphism over the algebraic closure of the ground field) in several families of curves of cryptograph ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/101357
Description: We prove a discrepancy bound “on average” over all initial values aα(0)=α of congruential pseudorandom numbers obtained from the sequences aα(n) over a finite field of prime order defined by aα(n)=naα ... More
Reviewed: Reviewed
Date: 2005
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81164
Description: 17 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/7841
Description: We give an explicit construction of circulant graphs of very high energy. This construction is based on Gauss sums. We also show the Littlewood conjecture can be used to establish new result for a cer ... More
Reviewed: Reviewed
Date: 2003
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/78679
Description: It is shown that the method of estimation of exponential sums with nonlinear recurring sequences, invented by the authors in a recent series of works, can be applied to estimating sums of multiplicati ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/82430
Description: 13 page(s)
Reviewed: Reviewed
Date: 2005
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81019
Description: 12 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2008
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/44748
Description: Abstract unavailable due to use of unsupported mathematical characters in the formatting.
Full Text: Full Text
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/135473
Description: We estimate the deviation of the number of solutions of the congruence. m²-n²≡c(modq),1≤m≤M,1≤n≤N, from its expected value on average over c=1,...,q. This estimate is motivated by the connection, rece ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130407
Description: Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y0) to the equation mx - ny = 1. E. I. Dinaburg and Y. G. Sinai have used continued fractions to show ... More
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/144589
Description: 11 page(s)
Full Text: Full Text
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/172365
Description: We give an upper bound on the number of vertices of the convex hull of the set of solutions to multivariate polynomial congruences modulo a prime p. The result is based on a combination of an estimate ... More
Reviewed: Reviewed