Brief CV of Kevin A. Broughan
Tertiary Education Record
MA Columbia University 1970
MPhil Columbia University 1975
Senior Science and
Teaching Assistant, Columbia University, 1969-70
Lecturer in Mathematics, University of Waikato, 1971-74,
Senior Lecturer: 1975-88,
Associate Professor: 1989-
Chairperson of Mathematics,
Dux of St. Bernard's College, 1960, 1961
NZ University National Scholarship, 1961
Applied Mathematics Prize,
Senior Scholarship in
Mathematics and Physics,
Sir George Grey Scholarship,
Fulbright Award for study in
UGC Postgraduate Scholar in Science, 1968
Columbia Ph.D. Qualifying Examination passed with Distinction, 1969
Faculty Fellowship, Columbia University, 1974-75
Senior Visiting Fellow,
Consultant to the research project on the Representation and
Manipulation of Mathematical Knowledge,
Steering Committee for High
Performance Computing -
Programme Committee for International Conference on Symbolic and
Algebraic Computation 1995
Department of Mathematics,
Fellow of the New Zealand Mathematical Society, elected 2001
Claude-McCarthy Fellowship 1994, 2004.
chair a session on number theory at ICM2006,
Invited participation in the American Institute of Mathematics workshop on the computational aspects of L-functions and modular forms, 2007.
of a special session on Number Theory, joint NZ Australian Mathematics
Memberships of Scholarly and Professional Societies:
American Mathematical Society (AMS),
Institute for Professional Engineers of New Zealand (IPENZ) designation M.IPENZ,
Research Publications since 2000
 R. E. D. Ferdinands, K. A. Broughan and H. Round, A time variant forward solution model of the bowling arm in cricket, Chapter in “Biomechanics Research in the New Millennium”, Routledge, 2002.
 K. A. Broughan appendix and associated software GL(n)pack in “Automorphic Forms and L-functions for the group GL(n,R)” by D. Goldfeld, Cambridge University Press, 2006.
Journal Articles published in refereed journals
 K. A. Broughan and Nan Zhu, “An integer programming problem with a linear programming solution”, Amer. Math. Monthly, 107, (2000), 444-446.
 K. A. Broughan, “The GCD-sum function”, Journal of Integer Sequences, 4, (2001), Article 01.2.2, (p1-19).
 K. A. Broughan, “Restricted Divisor Sums”, Acta Arithmetica, 101 (2002) p105-114.
 K. A. Broughan, “Vanishing of the integral of the Hurwitz Zeta function”, Bulletin of the Australian Mathematical Society, 65 (2002) p121-127.
 K. A. Broughan, “Asymptotic order of the square free part of n!”, Integers: Electronic Journal of Combinatorial Number Theory 2, A10, 2002, p1-6 .
 K. A. Broughan, “Adic topologies on the rational integers”, Canadian Journal of Mathematics, 55 (4) (2003) p711-723.
 K. A. Broughan and A. R. Barnett, “The homomorphic flow of the Riemann zeta function”, Math. Comp. 73 (2004), 987-1004.
 K. A. Broughan, “Holomorphic flows on simply connected subsets have no limit cycles”, Meccanica, 38 (2003), 699-709.
 K. A. Broughan, “Relations between the conductor and integer k’th root functions”, International Journal of Pure and Applied Mathematics, 5 (2003) p253-275).
 K. A. Broughan, “The structure of sectors of zeros of entire flows”, Topology Proceedings, 27 (2003), p379-394.
 K. A. Broughan, “Characterizing the sum of two cubes”, Journal of Integer Sequences, 6, (2003) Article 03.4.6, p1-7.
 K. A. Broughan, “Holomorphic flow of the Riemann Xi function”, Nonlinearity, 18, (2005), p1269-1294.
 K. A. Broughan and R. J. Casey, “Harmonic sets and the harmonic prime number theorem”, Bulletin of the Australian Mathematical Society , 71, (2005), p127-137.
 V. A. Krysko, J. Awrejcewicz, A. N. Kutsemako, K. Broughan, “Interaction between flexible shells (plates) and a moving lumped body”, Communications in Nonlinear Science and Numerical Simulation, 11 (2006), p13-43.
 K. A. Broughan and A. R. Barnett, “Linear law for the logarithms of the Riemann periods at simple critical zeros”, Mathematics of Computation, 75 (2006), p891-902.
 K. A. Broughan, Relaxations of the ABC conjecture using integer k’th roots, NZ Journal of Mathematics, 35 (2006), 121-136.
 K. A. Broughan and A. Ross Barnett, “Corrigendum to the holomorphic flow of the zeta function”, 76 (2007), p2249-2250.
 K. A. Broughan, “Corrigenda for holomorphic flows on simply connected regions have no limit cycles”, Meccanica, 42, (2007), p213.
 K. A. Broughan, “The average order of the Dirichlet series of the gcd-sum function”, Journal of Integer Sequences, (2007) Article 07.4.2 , p1-6.
 K. A. Broughan, “Computing Casimir operators for the generalized upper half plane”, International Journal of Pure and Applied Mathematics, 41 (2007), p549-560.
 K. A. Broughan and Qizhi Zhou, “Odd multiperfect numbers of abundancy 4”, Journal of Number Theory, 128 (2008), p1568-1575.
 K. A. Broughan, “Evaluating Jacquet’s GL(n) Whittaker function”, Mathematics of Computation, 78 (2009), p1061-1072.
 K. A. Broughan and A. Ross Barnett, “On primes with prime subscripts”, J. of Integer Sequences, 12 (2009) Article 09.2.3, p1-12.
Journal Articles accepted for publication in refereed journals
 K. A. Broughan, “Extension of the Riemann xi-functions logarithmic derivative positivity region to near the critical strip” Canadian Mathematical Bulletin, accepted 2006.
 K. Byard and K. A. Broughan, “Twelfth power residue difference sets”, Bull. Aust. Math. Soc, accepted 2008.
 Kevin A. Broughan, “An algorithm for the explicit evaluation of GL(n) Kloosterman sums”, Communications in Computer Algebra, accepted 2009.
 Kevin A. Broughan and A. Ross Barnett, “On the number of missing values of n! modulo p”, Journal of the Ramanujan Mathematical Society, accepted 2009.
Journal articles submitted for publication:
Gram lines and the average of the real part of the Riemann zeta function (with Ross Barnett)
A note on Lehmer’s Euler Phi function conjecture (with Jethro van Ekeren)
On flat primes and thin primes (with Zhou Qizhi)
Some Divisibility Properties of Binomial Coefficients and Wolstenholme's conjecture (with Florian Luca and Igor Shparlinski)
On the Furstenberg closure of a class of binary recurrences (with Florian Luca)
Conference Proceedings-Full written papers
 R. E. D. Ferdinands, K. A. Broughan, and H. Round, “Cricket Bowling: a two segment Lagrangian
model”, Proceedings of the 5th Australian conference on
Mathematics and Computers in Sport, 5M&CS,
 R. E. D. Ferdinands, K. A. Broughan, and H. Round, “Cricket Bowling: a two segment Lagrangian model”, Proceedings of the XVIII International Symposium on Biomechanics in Sports ISBS 2000, Hong Kong, 2000, p517-520.
 R. E. D. Ferdinands, K. A. Broughan, Howell Round, and Robert N. Marshall, “A fifteen-segment 3D rigid body model of bowling in cricket”, Proceedings of the international conference on Computer Simulation in Biomechanics, Hongkong, 2001, p99-104.
 K. A. Broughan, “Holomorphic Flows have no limit cycles”, Proceedings of the 6th
Conference on Dynamical Systems-Theory and Applications”,
 R. E. D. Ferdinands, R. N. Marshall, H. Round and K. A. Broughan,, “Bowling arm and trunk mechanics of fast bowlers in cricket”, Proceedings of the 4th Australasian Biomechanics Conference, T. M. Bach, D Orr, R. Baker and W. A. Sparrow eds., Melbourne, 2002, p176-177.
Published Abstracts of Presented Papers
 K. A. Broughan, “The ABC Conjecture”, NZ Mathematics Colloquium,
 K. A. Broughan, “Restricted Divisor Sums” Grand Challenges Conference of the AMS, UCLA, Abstracts of the 956th Meeting of the AMS, p34, 2000.
 R. E. D. Ferdinands, K. A. Broughan, H. Round, R. N. Marshall, “A fifteen-segment 3D rigid body model of bowling in cricket”, Book of abstracts of the International Society of Biomechanics XVIIIth Congress, Switzerland, 2001, p236.
 K. A. Broughan, “ The topological search for long arithmetic progressions”, Devonport
 K. A. Broughan and J. C. Turner, “The closure of the Fibonacci Numbers”,
The Tenth International Fibonacci Conference,
 K. A. Broughan, “The topological structure of holomorphic
flows in the neighbourhood of a centre”, 17th Summer Conference on Topology,
 K. A. Broughan, “Any non-commutative hyperbolic group of transformations of the upper
half plane acts discontinuously”, Devonport Topology Fest,
 K. A. Broughan, “Linear law for the logarithms of the Riemann zeta
function periods”, NZ Mathematics Colloquium,
 K. A. Broughan, “Colloquium Postscript: Universal Polish spaces and rendezvous numbers”,
Devonport Topology Fest,
 K. A. Broughan, “Zeta zeros and holomorphic flows”
International Congress of Mathematicians,
 K. A. Broughan, “Gram lines provide deep insight into the nature of the Riemann zeta
function”, NZ Mathematics Colloquium,
 K. A. Broughan, “Vassiliev invariants for proper and singular
knots”, Devonport Topology Fest,
 K. A. Broughan, “Vanishing
of the integral of the Hurwitz zeta function”, Joint NZMS AMS Conference,
 K. A. Broughan, “On a theorem in topological number theory describing the closure of
the Fibonacci numbers”, Devonport topology Fest,
 K. A. Broughan and A. R. Barnett, “On the missing values of n! mod p”, Joint Australian NZ Mathematics Convention, Christchurch 2008, collected abstracts.
 K. A. Broughan, “Gram lines and the average of the real part of the Riemann zeta function”, AMS Meeting Urbana-Champaign, 2009.
 K A Broughan, “Flat primes and thin primes”, AMS Meeting Urbana-Champaign, 2009.
 K A Broughan, “Tracking the Riemann zeta function with holomorphic flows”, UNAM Institute for
 K. A. Broughan, “Holomorphic flows and the Riemann zeta function”, CUNY Graduate Center Number
Deed of Assignment for the Naglink software system, Development Finance
Corporation and University of Waikato, 1984-87
Naglink Agreement for the distribution of the Naglink software system,
Numerical Algorithms Group and Development Finance Corporation, 1986
Developer Software Agreement for the use of Franz Lisp and Allegro CL
in distributed versions of SENAC, with Franz Inc (Berkeley), 1989
Software Distribution Agreement for the distribution of SENAC in UK/Europe
Software Distribution Agreement for the distribution of SENAC in North
Royalty sharing agreement for software and services with the Numerical
Algorithms Group (
Agreement with Numerical Recipes authors for the right to translate into
Lisp and use Numerical Recipes code in Senac, 1992.
Water Management Software research contract with ECNZ, 1992-1994.
Timetable Study for
Establishment of the NZ Mathematical Society, Foundation of the School of Computing and Mathematical Sciences at the University of Waikato, Academic staff representative on the University of Waikato Council (5 years), Member University Finance Committee (4 years), Member University Academic Board (10 years), Branch Chair of AUS (2 years) and National VP of AUS (1 year), establishment of the Bachelor of Engineering degree at the University of Waikato, Chair of the Department of Mathematics (6 years).
Kevin A. Broughan
17th April 2009