Notes on a generalized -conjecture over function fields
Notes on exponential-logarithmic terms
On completeness of left-invariant Lorentz metrics on solvable Lie groups.
We study geodesic completeness for left-invariant Lorentz metrics on solvable Lie groups.
On duality over a certain divided power algebra with positive characteristic.
On Sazonov Type Topology in p-adic Banach Space.
On the closed subfields of [...] Q ¯ p
Let p be a prime number, and let [...] Q¯ p be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.
On the Jacobian conjecture and the configurations of roots.
On the structure of compact subsets of ℂₚ
On valued function fields I.
Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.
Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).
Ostrwoski's theorem for Henselian valued skew fields.
-adic Siegel halfspace
Prolongement analytique à travers un T-filtre
Prolongement analytique en analyse -adique
Prolongement analytique en analyse -adique
Prolongement de la valeur absolue de Gauss et problème de Skolem
Puiseux series polynomial dynamics and iteration of complex cubic polynomials
We let be the completion of the field of formal Puiseux series and study polynomials with coefficients in as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in . We show that cubic polynomial dynamics over and are intimately related. More precisely, we establish that some elements of naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity) the quasiconformal...
Quelques questions ouvertes en analyse ultramétrique
Rapports de produits croulants
Reduction of semialgebraic constructible functions
Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.