A note on Waring's problem in p-adic fields
Algebraic points on cubic hypersurfaces
Anwendung eines abgeänderten Roth-Ridoutschen Satzes auf diophantische Gleichungen.
Artin's conjecture for septic and unidecic forms
Continued fractions of Laurent series with partial quotients from a given set
Diagonal forms of prime degree p in a P-adic ring
Effective bounds for the zeros of linear recurrences in function fields
In this paper, we use the generalisation of Mason’s inequality due to Brownawell and Masser (cf. [8]) to prove effective upper bounds for the zeros of a linear recurring sequence defined over a field of functions in one variable.Moreover, we study similar problems in this context as the equation , where is a linear recurring sequence of polynomials and is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].
Effectively computable bounds for the solutions of certain diophantine equations
Einige Sätze über p-adisohe Potenzreihen mit Anwendung auf gewisse exponentielle Gleichungen
Factorisation d'opérateurs différentiels à coefficients dans une extension liouvillienne d'un corps valué
On démontre ici un lemme de Hensel pour les opérateurs différentiels. On en déduit un théorème de factorisation pour des opérateurs différentiels à coefficients dans une extension liouvillienne transcendante d’un corps valué. On obtient en particulier un théorème de factorisation pour des opérateurs différentiels à coefficients dans une extension de par un nombre fini d’exponentielles et de logarithmes algébriquement indépendants sur .
Fermat's equation for matrices or quaternions over q-adic fields
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Generalized ABC theorems for non-Archimedean entire functions of several variables in arbitrary characteristic
Hadamard products of certain power series
Intermediate values and inverse functions on non-Archimedean fields.
Iterated exponents in number theory.
Le Veque's superelliptic equation over function fields
Local Diophantine Properties of Shimura Curves.
Local solvability of diagonal equations (again)
Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains
Let be a 2-dimensional normal excellent henselian local domain in which is invertible and let and be its fraction field and residue field respectively. Let be the set of rank 1 discrete valuations of corresponding to codimension 1 points of regular proper models of . We prove that a quadratic form over satisfies the local-global principle with respect to in the following two cases: (1) has rank 3 or 4; (2) has rank and , where is a complete discrete valuation ring with...