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Displaying 301 – 320 of 2019

Completely normal elements in some finite abelian extensions

Ja Koo, Dong Shin (2013)

Open Mathematics

We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.

Completion of r.t. extensions of local fields (I).

V. Alexandru, A. Popescu, N. Popescu (1996)

Mathematische Zeitschrift

Completion of r.t. extensions of local fields (II)

V. Alexandru, A. Popescu, N. Popescu (1998)

Rendiconti del Seminario Matematico della Università di Padova

Complexité et géométrie réelle

Jean-Jacques Risler (1984/1985)

Séminaire Bourbaki

Complexity bound of absolute factoring of parametric polynomials.

Ayad, A. (2004)

Zapiski Nauchnykh Seminarov POMI

Comportement local des fonctions continues sur un compact régulier d'un corps local

Eve Helsmoortel (1971)

Séminaire de théorie des nombres de Bordeaux

Composite n-forms and Cauchy kernels.

Konrad J. Heuvers, Pal Fischer (1987)

Aequationes mathematicae

Composite rational functions expressible with few terms

Clemens Fuchs, Umberto Zannier (2012)

Journal of the European Mathematical Society

We consider a rational function $f$ which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number $ℓ$ of terms. Then we look at the possible decompositions $f (x) = g (h (x))$ , where $g, h$ are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of $g$ is bounded only in terms of $ℓ$ (and we provide explicit bounds). This supports and quantifies the intuitive...