Irregular Primes and Integrality Theorems for Manifolds.
Isomorphic digraphs from powers modulo
Let be a prime. We assign to each positive number a digraph whose set of vertices is and there exists a directed edge from a vertex to a vertex if . In this paper we obtain a necessary and sufficient condition for .
Iterated Cesàro averages, frequencies of digits, and Baire category
Iterated digit sums, recursions and primality
We examine the congruences and iterate the digit sums of integer sequences. We generate recursive number sequences from triple and quintuple product identities. And we use second order recursions to determine the primality of special number systems.
Iterated exponents in number theory.
Iterating the sum-of-divisors function.
Jacobi sums and explicit reciprocity laws
Jacobi symbols, ambiguous ideals, and continued fractions
The purpose of this paper is to generalize some seminal results in the literature concerning the interrelationships between Legendre symbols and continued fractions. We introduce the power of ideal theory into the arena. This allows significant improvements over the existing results via the infrastructure of real quadratic fields.
Jak lze snáze a jistěji děliti nežli způsobem obyčejným?
Jednočlenné perioda zbytků z mocnin s předcházejícími členy
Jednoduché důkazy některých vět o kmenných číslech
Ještě o kvadratických polynomech nabývajících mnoha prvočíselných hodnot
Kamke, E., Zur Arithmetik der Polynome
Kettenbrüche als Summen ebensolcher
Klein polyhedra and lattices with positive norm minima
A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of . 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 Klein polyhedra generated by a lattice have uniformly bounded determinants...
Kongruenzen zwischen Koeffizienten trigonometrischer Reihen und Klassenzahlen quadratisch imaginärer Körper.
Konstruktion von Klassenkörpern und Potenzrestkriterien für quadratische Einheiten.
Konvergenz von Teilen der harmonischen Reihe.
Kriterien für n-te Potenzreste.
Kummer congruences for expressions involving generalized Bernoulli polynomials
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.