Displaying similar documents to “Solving Diophantine Problems Modulo Every Prime”

Remarques sur le premier cas du théorème de Fermat sur les corps de nombres

Alain Kraus (2015)

Acta Arithmetica

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The first case of Fermat's Last Theorem for a prime exponent p can sometimes be proved using the existence of local obstructions. In 1823, Sophie Germain obtained an important result in this direction by establishing that, if 2p+1 is a prime number, the first case of Fermat's Last Theorem is true for p. In this paper, we investigate such obstructions over number fields. We obtain analogous results on Sophie Germain type criteria, for imaginary quadratic fields. Furthermore, extending...

Comportement local moyen de la fonction de Brjuno

Michel Balazard, Bruno Martin (2012)

Fundamenta Mathematicae

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We describe the average behaviour of the Brjuno function Φ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of Φ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of Φ.

Wronskien et équations différentielles p-adiques

Jean-Paul Bézivin (2013)

Acta Arithmetica

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We prove an inequality linking the growth of a generalized Wronskian of m p-adic power series to the growth of the ordinary Wronskian of these m power series. A consequence is that if the Wronskian of m entire p-adic functions is a non-zero polynomial, then all these functions are polynomials. As an application, we prove that if a linear differential equation with coefficients in ℂₚ[x] has a complete system of solutions meromorphic in all ℂₚ, then all the solutions of the differential...