Now showing items 1-5 of 39

  • An Algorithm for the explicit evaluation of GL(n, R) Kolsterman sums

    Broughan, Kevin A. (Association for Computing Machinery, 2009)
    An algorithm for the explicit evaluation of Kloosterman sums for GL(n, R) for n ≥2 and an implementation in the Mathematics package GL(n) pack are described
  • Appendix: The GL(n) pack Manual

    Broughan, Kevin A. (Cambridge University Press, 2006)
    This appendix is the manual for a set of functions written to assist the reader to understand and apply the theorems on GL(n, R) set out in the main part of the book. The software for the package is provided over the World ...
  • Asymptotic order of the square free part of n!

    Broughan, Kevin A. (2002)
    The asymptotic order of the logarithm of the square-free part of n! is shown to be (log 2)n with error O(√n ).
  • The average order of the Dirichlet series of the gcd-sum function

    Broughan, Kevin A. (University of Waterloo, Department of Computer Science, 2007)
    Using a result of Bordellès, we derive the second term and improved error expressions for the partial sums of the Dirichlet series of the gcd-sum function, for all real values of the parameter.
  • The boundedness principle characterizes second category subsets

    Broughan, Kevin A. (1977)
    Converses are proved for the Osgood (the Principle of Uniform Boundedness), Dini, and other well known. theorems. The notion of a continuous step function on a topological space is defined and a class of spaces identified ...

Showing up to 5 theses - most recently added to Research Commons first.

  • Critical sets of full Latin squares

    Raass, Petelo Vaipuna (University of Waikato, 2016)
    This thesis explores the properties of critical sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes. In Chapter 3 we study ...
  • Brocard's problem and variations

    Liu, Yi (University of Waikato, 2013)
    This thesis examines the work which has been done on Brocard’s problem which is to study solutions to n! + 1 = x², and related problems of the form n! = f(x) or n! = f(x, y), where f is a polynomial with integer ...
  • Comparison between the RSA cryptosystem and elliptic curve cryptography

    Abdullah, Kamilah (The University of Waikato, 2010)
    In the globalization era, cryptography becomes more popular and powerful; in fact it is very important in many areas (i.e. mathematics, computer science, networks, etc). This thesis provides an overview and comparison ...
  • Multiply perfect numbers of low abundancy

    Zhou, Qizhi (University of Waikato, 2010)
    The purpose of this thesis is to investigate the properties of multiperfect numbers with low abundancy, and to include the structure, bounds, and density of certain multiperfect numbers. As a significant result of this ...