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An approach to Julia Robinson numbers through the lattice of subfields
Xavier Vidaux, Carlos R. Videla
By fully describing the lattice of subfields of some towers of number fields built by iterating square roots, we obtain infinitely many fields, each of them either contradicts Juli…
Effectivity for existence of rational points is undecidable
Natalia Garcia-Fritz, Hector Pasten, Xavier Vidaux
The analogue of Hilbert's tenth problem over asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as o…
Optimal bounds for Büchi's problem in modular arithmetic II
Pablo Sáez, Xavier Vidaux, Maxim Vsemirnov
Given a prime and an integer , we show that there exists an integer such that for any quadratic polynomial with coefficients in the ring of integers modulo $…
Dedekind's criterion for the monogenicity of a number field versus Uchida's and Lüneburg's
Xavier Vidaux, Carlos R. Videla
We compare three different characterizations, due respectively to R. Dedekind, K. Uchida, and H. Lüneburg, of when is the ring of integers of , and app…
Julia Robinson numbers and arithmetical dynamic of quadratic polynomials
Marianela Castillo Fernández, Xavier Vidaux, Carlos R. Videla
For rings of totally real algebraic integers, J. Robinson defined a set which is always or of the form or for some real nu…
A characterization of Büchi's integer sequences of length 3
Pablo Saéz, Xavier Vidaux
We give a new characterization of generalized Büchi sequences (sequences whose sequence of squares has constant second difference , for some fixed integer ) of length 3 ove…