Kevin A. Broughan

Office: G3.27 Email: broughan.kevin@gmail.com Address: Emeritus Professor Kevin Broughan Department of Mathematics School of Computing and Mathematical Sciences University of Waikato Private Bag 3105 Hamilton New Zealand Phone: +64-7-838 4713 (CMS School Office) Image Credit: Jackie Broughan, Rio de Janiero, 2018.

• Mathematics news from the AMS.
• My mathematical ancestors back to Gauss and Euler.
• A brief CV.
• Submissions to various bodies and Letters to the Editors of NZ newspapers and magazines.
• Democracy Documents, Links to webpages and sites supporting the democracy movement in New Zealand, 2023.
• Professor Daniel Delbourgo, PhD Cambridge, Principal Tutor for Daniel's Maths Tuition. Assistance with all levels of mathematics.
• Climate change links. It includes climate change news from the main stream international media, a selection of Ted talks, visualizations from major institutes, Wikipedia links and descriptions of some introductory expository books.
• Climate change models: under development. It will include links for the github online repository, the Julia Language, the CliMA project at MIT, Caltec and JPL, books I on geophysical fluid dyamics and advanced topics such as turbulence, a set of equations and numerical methods for climate change, and links to other models.

Equivalents of the Riemann hypothesis

• Main page for the three volume work published by Cambridge University Press in 2017 and 2023.

  The page includes links to the Cambridge web pages for the books, an ICM2019 poster, the main equivalents to RH from volumes one and two in diagram form, RHpack and GRHpack software, a webinar of the author interviewed by Lisa Farkas, Errata and notes, and reviews, including 5 for volumes one and two and three cover reviews for volume three.

Bounded gaps between primes: the epic breakthroughs of the early 21st century

• Main page for the 590 page work published by Cambridge in 2021.

  The page includes links to the Cambridge web page for the book, the PGpack software, a set of annotated links for the human backstory to the breakthroughs, reviews and comments, and a page of Errata and Notes.

• Recent publications and preprints.
• Shifted and balanced primes examples.
• Slides for the lecture "Holomorphic flows and the Riemann zeta function" given in 2009.
• Phase portraits of the Riemann zeta function zeros.
• Beamer slides for "Small prime gaps", University of Auckland, 6 December 2017.

• RHpack: software for "Equivalents of the Riemann hypothesis, Volume One: Arithmetic Equivalents" (CUP - 2017).
• GRHpack: software for "Equivalents of the Riemann hypothesis: Volume Two: Analytic Equivalents" (CUP - 2017).
• GL(n)pack: software for "Automorphic forms and L-functions for the group GL(n,R)", Dorian Goldfeld, (CUP - 2006).
• PGpack: software for "Bounded gaps between primes: the epic breakthroughs of the early 21st century" (CUP - 2021).
• f2cl: software to translate a class of Fortran77 programs to Common Lisp, with Diane Koorey Wilcock.
• Senac: a software environment for numeric and algebraic computation, with Steve Galbraith, Marty Glanvill, Diane Koorey Wilcock, Wayne Schou, Richard Shepherd, and Nan Zhou. Includes algrebraic algorithms, Risch Integration, a symbolic numeric interface to the NAG Library, Numerical Recipies, finite elements etc. Senac is now in recess.

• Number Theory Web
• Unsolved Problems in Mathematics from Wikipedia
• History of Mathematics Web Archive
• University of Waikato Department of Mathematics
• University of Waikato Library
• University of Auckland Department of Mathematics
• Columbia University Department of Mathematics
• New Zealand Mathematical Society
• American Mathematical Society
• MathSciNet
• Google Search
• Mathematics Genealogy Project
• Prof Steve Galbraith's elliptic curve cryptography blog

• Level one: Introduction to Calculus MATH101-10B
• Level two: Linear Algebra inner product module MATHS202-18A
• Level two: Elements of Analysis MATH252-10B
• Level three: Modern Algebra MATH310-10A
• Level three: Topics in Pure Mathematics MATH319-11A
• Level five: Metric Spaces MATH501-18A
• Level five: Number Theory MATH509-16A

• Gauss-Dirichlet Gottingen 2005 conference - images.
• AIM Workshop on L-functions and Modular Forms, August 2007 - images.
• Joint NZ AMS meeting Wellington December 2007 - images.
• Devonport Topology Fest in honour of Ivan Reilly's retirement 2008 - images .
• Marist Group of 1962, 50th anniversary reunion - images,

• Jude Broughan homepage
• Waikato Society of the Arts
• Judith Devons
• Metropolitan Museum of Art
• MoMA The Museum of Modern Art
• WebMuseum: Paris

• Blackbirds mating dance