Les ensembles de Bésineau
Michel Mendès France (1973-1974)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Michel Mendès France (1973-1974)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Andrzej Schinzel (1961)
Acta Arithmetica
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Georges Rhin (1967-1968)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Georges Rhin (1976-1977)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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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...
Marthe Grandet-Hugot (1976-1977)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Philippe Toffin (1976-1977)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Michel Mendès France (1964-1965)
Séminaire Dubreil. Algèbre et théorie des nombres
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Jean-Loup Mauclaire (1973-1974)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Jan Denef (1990-1991)
Séminaire Bourbaki
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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.
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...