Computation of 2-groups of positive classes of exceptional number fields

Jean-François Jaulent; Sebastian Pauli; Michael E. Pohst; Florence Soriano–Gafiuk

Displaying similar documents to “Computation of 2-groups of positive classes of exceptional number fields”

Thomas’ conjecture over function fields

Volker Ziegler (2007)

Journal de Théorie des Nombres de Bordeaux

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Thomas’ conjecture is, given monic polynomials $p_{1},$ $..., p_{d} \in ℤ [a]$ with $0 < deg p_{1} < \dots < deg p_{d}$ , then the Thue equation (over the rational integers) $(X - p_{1} (a) Y) \dots (X - p_{d} (a) Y) + Y^{d} = 1$ has only trivial solutions, provided $a \geq a_{0}$ with effective computable $a_{0}$ . We consider a function field analogue of Thomas’ conjecture in case of degree $d = 3$ . Moreover we find a counterexample to Thomas’ conjecture for $d = 3$ .

Formulae for the singularities at infinity of plane algebraic curves.

Gwoździewicz, Janusz, Płoski, Arkadiusz (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Approximation exponents for algebraic functions in positive characteristic

Bernard de Mathan (1992)

Acta Arithmetica

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In this paper, we study rational approximations for algebraic functions in characteristic p > 0. We obtain results for elements satisfying an equation of the type $α = (A α^{q} + B) / (C α^{q} + D)$ , where q is a power of p.

Small generators of function fields

Martin Widmer (2010)

Journal de Théorie des Nombres de Bordeaux

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Let $𝕂 / k$ be a finite extension of a global field. Such an extension can be generated over $k$ by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.

The fluctuations in the number of points on a family of curves over a finite field

Maosheng Xiong (2010)

Journal de Théorie des Nombres de Bordeaux

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Let $l \geq 2$ be a positive integer, $𝔽_{q}$ a finite field of cardinality $q$ with $q \equiv 1 (mod l)$ . In this paper, inspired by [, , ] and using a slightly different method, we study the fluctuations in the number of $𝔽_{q}$ -points on the curve $ℂ_{F}$ given by the affine model $ℂ_{F} : Y^{l} = F (X)$ , where $F$ is drawn at random uniformly from the set of all monic $l$ -th power-free polynomials $F \in 𝔽_{q} [X]$ of degree $d$ as $d \to \infty$ . The method also enables us to study the fluctuations in the number of $𝔽_{q}$ -points on the same family of curves arising from the set of monic...

The coincidence Nielsen number for maps into real projective spaces

Jerzy Jezierski (1992)

Fundamenta Mathematicae

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We give an algorithm to compute the coincidence Nielsen number N(f,g), introduced in [DJ], for pairs of maps into real projective spaces.

Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

Aaron Levin (2007)

Journal de Théorie des Nombres de Bordeaux

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We study the problem of constructing and enumerating, for any integers $m, n > 1$ , number fields of degree $n$ whose ideal class groups have “large" $m$ -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.