-algebre -adiche e loro rappresentazioni
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Mario Poletti (1972)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Matija Kazalicki (2011)
Acta Arithmetica
Maurizio Monge (2014)
Journal de Théorie des Nombres de Bordeaux
Let be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree over , and extend it to when the base fields is an unramified extension of .When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We derive a complete classification...
M. Auslander, K.W. Roggenkamp (1972)
Inventiones mathematicae
Benjamin Dupuy (2007)
Acta Arithmetica
Luca Caputo (2007)
Journal de Théorie des Nombres de Bordeaux
Let be a finite extension of and be the set of the extensions of degree over whose normal closure is a -extension. For a fixed discriminant, we show how many extensions there are in with such discriminant, and we give the discriminant and the Galois group (together with its filtration of the ramification groups) of their normal closure. We show how this method can be generalized to get a classification of the extensions in .
Martin, Roland (1995)
Experimental Mathematics
Robert L. Benedetto (2014)
Acta Arithmetica
Let K be a nonarchimedean field, and let ϕ ∈ K(z) be a polynomial or rational function of degree at least 2. We present a necessary and sufficient condition, involving only the fixed points of ϕ and their preimages, that determines whether or not the dynamical system ϕ: ℙ¹ → ℙ¹ has potentially good reduction.
Peter Roquette (1977)
Journal für die reine und angewandte Mathematik
Wiliam G. McCallum (1995)
Journal für die reine und angewandte Mathematik
David Ford, Sebastian Pauli, Xavier-François Roblot (2002)
Journal de théorie des nombres de Bordeaux
We present an algorithm that returns a proper factor of a polynomial over the -adic integers (if is reducible over ) or returns a power basis of the ring of integers of (if is irreducible over ). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.
S. Turner (1990)
Inventiones mathematicae
Yoshihiro Koya (1990)
Inventiones mathematicae
Ralph Greenberg (1973)
Inventiones mathematicae
Masatoshi Ikeda (1972)
Journal für die reine und angewandte Mathematik
Robert C. Valentini, Manohar L. Madan (1980)
Journal für die reine und angewandte Mathematik
Rodney I. Yager (1982)
Compositio Mathematica
Hervé Jacquet, Joseph Shalika (1985)
Mathematische Annalen
Takashi Taniguchi (2008)
Annales de l’institut Fourier
Let be a number field. In this paper, we give a formula for the mean value of the square of class number times regulator for certain families of quadratic extensions of characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pairs of quaternion algebras. We also prove an asymptotic formula of the correlation coefficient for class number times regulator of certain families of quadratic extensions.
James Borger (2004)
Journal de Théorie des Nombres de Bordeaux
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
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