Recent Preprints and Publications

These are all in PDF format. For full details on the publication status of any item in the list below contact Kevin Broughan at kab@waikato.ac.nz

  • The holomorphic flow of the Riemann zeta function, with A. R. Barnett, (Mathematics of Computation, vol 73 (2004), p987-1004.)

  • Corrigendum for "The holomorphic flow of the Riemann zeta function", with A. R. Barnett, (to appear in Mathematics of Computation).

  • Corrigendum II for "The holomorphic flow of the Riemann zeta function", with A. R. Barnett, (preprint).

  • Phase portraits of the zeros of the Riemann Zeta function, (web data base).

  • Phase portraits of the zeros of the Riemann Xi function, (web data base).

  • Holomorphic flows on simply connected regions have no limit cycles, Meccanica, vol 38 (2003), p699-709.

  • Corrigenda for "Holomorphic flows on simply connected regions have no limit cycles", Meccanica, vol 42 (2007) p213.

  • The gcd-sum function, Journal of Integer Sequences, vol 4 (2002) Article 01.2.2, p1-19.

  • Restricted divisor sums, Acta Arithmetica, vol 101, (2002), p105-114.

  • Relationships between the integer conductor and k'th root functions, International Journal of Pure and Applied Mathematics, vol 5 (2003), p253-275.

  • Vanishing of the integral of the Hurwitz zeta function, Bulletin of the Australian Mathematical Society, vol 65 (2002) p121-127.

  • Adic topologies for the rational integers,, Canadian Journal of Mathematics, vol 55 (2003), p711-723.

  • Characterizing the sum of two cubes, Journal of Integer Sequences, vol 6 (2003), Article 03.4.6, p1-7.

  • Asymptotic order of the square free part of n!, Integers: The Electronic Journal of Combinatorial Number Theory, vol 2, A10, (2002), p1-6.

  • Relaxations of the ABC conjecture using integer k'th roots, New Zealand Journal of Mathematics, vol 35 (2006), p121-136.

  • The structure of sectors of zeros of entire flows Topology Proceedings, vol 27 (2003), p379-394.

  • Holomorphic flow of Riemann's function Xi(s) Nonlinearity, vol 18, (2005), p1269-1294.

  • Square free factoring of rational integers and beyond, with T. E. Stokes, (preprint).

  • Linear law for the logarithms of the Riemann periods at simple critical zeta zeros, with A. R. Barnett, Mathematics of Computation, vol 75 (2006), p891-902.

  • Extension of the Riemann xi-function's logarithmic derivative positivity region to near the critical strip, Canadian Mathematical Bulletin (to appear).

  • Harmonic sets and the harmonic prime number theorem, with R. J. Casey, Bulletin of the Australian Math. Soc. vol 71, (2005), p127-137.

  • The average order of the Dirichlet series of the gcd-sum function, Journal of Integer Sequences, vol 10, (2007), Article 07.4.2, p1-6.

  • Odd multiperfect numbers of abundancy four, with Qizhi Zhou, vol 128 (2008), p1568-1575.

  • Gram lines and the average of the real part of the Riemann zeta function, with A. Ross Barnett, (preprint).

  • Computing Casimir operators for the generalized upper half plane, International Journal of Pure and Applied Mathematics, 41 (2007), p549-560.

  • Evaluating Jacquet’s GL(n) Whittaker function, Mathematics of Computation, 78 (2009), p1061-1072.

    On primes with prime subscripts, with A. Ross Barnett, J. of Integer Sequences, 12 (2009) Article 09.2.3, p1-12.

  • Twelfth power residue difference sets, with K. Byard, Bull. Aust. Math. Soc., (to appear).

  • An algorithm for the explicit evaluation of GL(n) Kloosterman sums, Communications in Computer Algebra, (to appear).

  • On the number of missing values of n! modulo p, with A. Ross Barnett, Journal of the Ramanujan Mathematical Society, (to appear).

  • A note on Lehmer’s Euler Phi function conjecture, with Jethro van Ekeren, (preprint).

  • On flat primes and thin primes, with Zhou Qizhi, (preprint).

  • Some Divisibility Properties of Binomial Coefficients and Wolstenholme's conjecture, with Florian Luca and Igor Shparlinski, (preprint).

  • On the Furstenberg closure of a class of binary recurrences, with Florian Luca, (preprint).

    Last modified: 17th April 2009.