On algebraic solutions of algebraic Pfaff equations

Henryk Żołądek

Displaying similar documents to “On algebraic solutions of algebraic Pfaff equations”

The algebraic independence of Weierstrass functions and some related numbers

W. Brownawell, K. Kubota (1977)

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Uniformization of a class of algebraic functions of the third degree by the method of differential equations

J. Janikowski (1967)

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Transcendence results on the generating functions of the characteristic functions of certain self-generating sets, II

Peter Bundschuh, Keijo Väänänen (2015)

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This article continues a previous paper by the authors. Here and there, the two power series F(z) and G(z), first introduced by Dilcher and Stolarsky and related to the so-called Stern polynomials, are studied analytically and arithmetically. More precisely, it is shown that the function field ℂ(z)(F(z),F(z⁴),G(z),G(z⁴)) has transcendence degree 3 over ℂ(z). This main result contains the algebraic independence over ℂ(z) of G(z) and G(z⁴), as well as that of F(z) and F(z⁴). The first...

On polynomial transformations II

W. Narkiewicz (1962)

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A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions

S. C. Coutinho (2007)

Annales de l’institut Fourier

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We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.

Algebraic numbers near the unit circle

C. Lloyd-Smith (1985)

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On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

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Given integers $D > 0, n > 1, 0 < r < n$ and a constant $C > 0$ , consider the space of $r$ -tuples $\vec{P} = (P_{1} ... P_{r})$ of real polynomials in $n$ variables of degree $\leq D$ , whose coefficients are $\leq C$ in absolute value, and satisfying $\det {(\frac{\partial P_{i}}{\partial x_{i}} (0))}_{1 \leq i, j \leq r} = 1$ . We study the family ${f | V}$ of algebraic functions, where $f$ is a polynomial, and $V = {| x | \leq δ, \vec{P} (x) = 0}, δ > 0$ being a constant depending only on $n, D, C$ . The main result is a quantitative extension theorem for these functions which is uniform in $\vec{P}$ . This is used to prove Bernstein-type inequalities which are again uniform with respect to $\vec{P}$ . ...

On the space of morphisms into generic real algebraic varieties

Riccardo Ghiloni (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let $Z$ be a real algebraic variety. We say that $Z$ is generic if there exist a finite family ${D_{i}}_{i = 1}^{n}$ of irreducible real algebraic curves with genus $\geq 2$ and a biregular embedding of $Z$ into the product variety $\prod_{i = 1}^{n} D_{i}$ . A bijective map $ϕ : {\tilde{Z}}^{} \to Z$ from a real algebraic variety $\tilde{Z}$ to $Z$ is called weak change of the algebraic structure of $Z$ if it is regular and its inverse is a Nash map. Generic real algebraic...