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 . . . . . . . . . . . . . . .
Beiträge zu einer additiven Zahlentheorie [Book]
Binary quadratic forms and sums of triangular numbers
Blocks for symmetric groups and their covering groups and quadratic forms.
Congruences for and
Congruences for certain families of Apéry-like sequences
We systematically investigate the expressions and congruences for both a one-parameter family as well as a two-parameter family of sequences.
Congruences for
Let ℤ be the set of integers, and let (m,n) be the greatest common divisor of the integers m and n. Let p ≡ 1 (mod 4) be a prime, q ∈ ℤ, 2 ∤ q and p=c²+d²=x²+qy² with c,d,x,y ∈ ℤ and c ≡ 1 (mod 4). Suppose that (c,x+d)=1 or (d,x+c) is a power of 2. In this paper, by using the quartic reciprocity law, we determine in terms of c,d,x and y, where [·] is the greatest integer function. Hence we partially solve some conjectures posed in our previous two papers.
Construction of entire modular forms of weights 5 and 6 for the congruence group .
Correlations of representation functions of binary quadratic forms
Cyclic polygons of integer points
Darstellungsmaße indefiniter quadratischer Formen.
Démonstration élémentaire d'un théorème énoncé par M. E. Catalan