A combinatorial proof of a result from number theory.
A note on the representability of quaternary quadratic forms as sums of squares of two linear forms
A restricted Epstein zeta function and the evaluation of some definite integrals
Algorithme de multiplicativité des sommes de carrés
An arithmetic formula of Liouville
An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.
An odd square as a sum of an odd number of odd squares
Analogues of Jacobi's two-square theorem: an informal account.
Antieigenvalue analysis for continuum mechanics, economics, and number theory
My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...
Arithmetical equivalents for a remarkable identity between theta functions . . . . . . . . . . . . . . .