Arithmetical properties of certain infinite products

On the Arithmetical Properties of Certain Entire Characteristic Functions

Three Term Identities for the Coefficients of Certain Infinite Products

Arithmetical Properties of Polynomials

1. Throughout this paper f (x) will denote a polynomial whose coefficients are integers with highest common factor 1, and 1 will denote the degree of f (x). We assume that the highest coefficient in f (x) is positive. It has been known for some time that if f (x) is not the l-th 'power of a linear polynomial with integral coefficients then there are infinitely ,

Structure of Certain Banach Algebra Products

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.

Arithmetical Congruence Preservation: From Finite to Infinite

Various problems on integers lead to the class of functions defined on a ring of numbers (or a subset of such a rings) METTRE RING AU SINGULIER and verifying a − b divides f(a) − f(b) for all a, b. We say that such functions are “congruence preserving”. In previous works, we characterized these classes of functions for the cases N → Z, Z→ Z and Z/nZ→ Z/mZ in terms of sums series of rational pol...