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5 papers · 1 filter
Most totally real fields do not have universal forms or Northcott property
Nicolas Daans, Vitezslav Kala, Siu Hang Man +2
We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott prope…
On Diophantine equations involving sums of Fibonacci numbers and powers of
Kwok Chi Chim, Volker Ziegler
In this paper, we completely solve the Diophantine equations and , where d…
Distribution of factorials modulo p
Oleksiy Klurman, Marc Munsch
We prove that the sequence occupies at least residue classes in the short interval and improving prev…
Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials
Dijana Kreso, Robert F. Tichy
Starting from Ritt's classical theorems, we give a survey of results in functional decomposition of polynomials and of applications in Diophantine equations. This includes sufficie…
Small generators of function fields
Martin Widmer
Let be a finite extension of a global field. Such an extension can be generated over by a single element. The aim of this article is to prove the existence of a "small" g…