Uniformly counting rational points on conics
We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over ℚ. The estimate is uniform in the coefficients of the underlying quadratic form.
Unisequences and nearest integer continued fraction midpoint criteria for Pell's equation.
Unités relatives
Units generating the ring of integers of complex cubic fields
All purely cubic fields such that their maximal order is generated by its units are determined.
Universality of a non-classical integral quadratic form over ℚ(√5)
Unsolvability of the Pell minus-equation for certain odd discriminants
Untere Schranken für Lösungen der Fermatschen Gleichung
Upper bounds for the degrees of decomposable forms of given discriminant
1. Introduction. In our paper [5] a sharp upper bound was given for the degree of an arbitrary squarefree binary form F ∈ ℤ[X,Y] in terms of the absolute value of the discriminant of F. Further, all the binary forms were listed for which this bound cannot be improved. This upper estimate has been extended by Evertse and the author [3] to decomposable forms in n ≥ 2 variables. The bound obtained in [3] depends also on n and is best possible only for n = 2. The purpose of the present paper is to establish...
Using Lucas sequences to generalize a theorem of Sierpiński
Úvod do elementární teorie číselné [Book]
Values of isotropic quadratic forms at -integral points
Values of quadratic forms at primitive integral points.
Variants of the Brocard-Ramanujan equation
In this paper, we discuss variations on the Brocard-Ramanujan Diophantine equation.
Variationen über ein diophantisches Thema.
Variations on a theme of Runge: effective determination of integral points on certain varieties
We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application of our...
Variations on Euclid's formula for perfect numbers.
Variations sur un thème de Carl Runge
Variations sur un thème de Mahler.
Verifizierung des symmetrischen Teils der Fermatschen Vermutung für unendlich viele paarweise teilerfremde Exponenten E.
Von Polyedern im ganzzahligen Gitter.