Page 1

Displaying 1 – 11 of 11

Showing per page

Klein polyhedra and lattices with positive norm minima

Oleg N. German (2007)

Journal de Théorie des Nombres de Bordeaux

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of n . It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved that the facets of all the 2 n Klein polyhedra generated by a lattice Λ have uniformly bounded determinants...

Kummer congruences for expressions involving generalized Bernoulli polynomials

Glenn J. Fox (2002)

Journal de théorie des nombres de Bordeaux

We illustrate how a particular expression, involving the generalized Bernoulli polynomials, satisfies systems of congruence relations if and only if a similar expression, involving the generalized Bernoulli numbers, satisfies the same congruence relations. These congruence relations include the Kummer congruences, and recent extensions of the Kummer congruences provided by Gunaratne.

Currently displaying 1 – 11 of 11

Page 1