Dept of Mathematics and Statistics, Lancaster University

My departmental page (with contact information)

- Banach spaces and operator ideals
- Inequalities and special functions
- (very) analytic number theory

Book "The Prime Number Theorem" Cambridge University Press 2003

Elliptic integrals, the arithmetic-geometric mean and the Brent-Salamin algorithm for π

Inequalities for the perimeter of an ellipse (Math. Gazette, 2014)

A fresh look at Euler's limit formula for the gamma funnction (Math. Gazette, 2014)

Series involving $\zeta (n)$ (Math.\ Gazette, 2014)

Some inequalities for $(a+b)^p$ and $(a+b)^p + (a-b)^p$ (Math. Gazette, 2014)

Inequalities comparing $(a+b)^p - a^p - b^p$ and $a^{p-1}b + ab^{p-1}$

Notes on Fermat's Last Theorem

Hilbert's inequality and related results

Counting zeros of generalized polynomials: Descartes' rule of signs and Laguerre's extensions

Two squares and four squares: the simplest proof of all?

Even and odd square-free numbers

Counting divisors (Math. Gazette, 2014)

Operator-valued extensions of matrix-norm inequalities

Carmichael numbers with three prime factors

Carmichael numbers and pseudoprimes

Interpolating polynomials and divided differences

An inequality for 3-factor Carmichael numbers due to J.M. Chick

Euler, Ioachimescu and the trapezium rule

Some remarkable integrals derived from a simple algebraic identity

My son Tim (alias Timothy or T.P.) died tragically on 5 September 2013. He was passionately keen on mathematics, though he did not complete a Ph. D. or hold a paid position.

The following is a selection of his mathematical writings, both published and unpublished, The unpublished ones were generally notes intended only for his own use, but some of them may be of interest to a wider audience. Most of them lacked a list of references which I have endeavoured to supply.

The probability integral by volume of revolution (Math. Gazette, 1994)

Another proof that zeta(2) = pi^2/6 by double integration (Math Gazette, 2013)

Orbits made easy by complex numbers (Math. Gazette, 2014)

Some double series related to zeta(3) (Math. Gazette, 2014)

Polylogarithms, multiple zeta values, and the series of Hjortnaes and Comtet

An elementary derivation of the Poisson summation formula

The fourth power moment of zeta(1/2 + it)

The approximate functional equation for zeta(s)^2

The Ingham-Huxley zero-density theorem

Linnik's proof of the Waring-Hilbert theorem from Hua's book (with a mistake corrected)

The Gauss circle problem (the classical exponent 1/3)

Integrating the error in the divisor problem

Daboussi's version of Vinogradov's bound for the exponential sum over primes

Member of Lancaster Baptist Church and church representative for Christian Aid

Mountain walking (not hard climbing!)

Member of Austrian
Alpine Club

Articles on mountain walking:

- The Japan Alps (Austrian Alpine Club Newsletter 73, 1982)
- Jotunheimen (Austrian Alpine Club Newsletter 97, 1988)
- Introducing the Children to the Alps (1989)
- The Schladminger Tauern (Austrian Alpine Club Newsletter 130, 1996), revised and expanded 2002
- The Lochaber Traverse (1996)
- Kilimanjaro (2003)

Scottish dancing

instructor of class at Hest
Bank (Tuesdays 7.30 p.m.)

holder of teaching certificate
of the Royal Scottish Country Dance Society

Running

best marathon time 2:54:37
(Wolverhampton, 1983 - now a long time ago!)

How old am I? (simple number games)