scholarly journals Linear nested Artin approximation theorem for algebraic power series

2018 ◽  
Vol 158 (1-2) ◽  
pp. 55-73
Author(s):  
Francisco-Jesús Castro-Jiménez ◽  
Dorin Popescu ◽  
Guillaume Rond
Keyword(s):  
Power Series ◽  
Approximation Theorem ◽  
Artin Approximation ◽  
Algebraic Power Series

A Gap Theorem for Differentially Algebraic Power Series

Number Theory ◽  
1991 ◽  
pp. 211-214
Author(s):  
Leonard Lipshitz ◽  
Lee A. Rubel
Keyword(s):  
Power Series ◽  
Gap Theorem ◽  
Algebraic Power Series

scholarly journals Echelons of power series and Gabrielov's counterexample to nested linear Artin approximation

2018 ◽  
Vol 50 (4) ◽  
pp. 649-662
Author(s):  
Mariemi E. Alonso ◽  
Francisco J. Castro-Jiménez ◽  
Herwig Hauser ◽  
Christoph Koutschan
Keyword(s):  
Power Series ◽  
Artin Approximation

Bernstein Power Series

1964 ◽  
Vol 16 ◽  
pp. 241-252 ◽  
Author(s):  
E. W. Cheney ◽  
A. Sharma
Keyword(s):  
Power Series ◽  
Infinite Series ◽  
Approximation Theorem ◽  
Bernstein Polynomials ◽  
Starting Point ◽  
Image Position ◽  
Weierstrass Approximation Theorem

In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomialsare constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared. It is our purpose here to consider several generalizations in the form of infinite series and to establish some of their properties.

scholarly journals REMARKS ON EISENSTEIN

2013 ◽  
Vol 94 (2) ◽  
pp. 158-180 ◽  
Author(s):  
YURI BILU ◽  
ALEXANDER BORICHEV
Keyword(s):  
Power Series ◽  
Number Field ◽  
Laurent Series ◽  
Quantitative Version ◽  
Algebraic Power Series

AbstractWe obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients.

Continued Fractions of Algebraic Power Series in Characteristic 2

1976 ◽  
Vol 103 (3) ◽  
pp. 593 ◽  
Author(s):  
Leonard E. Baum ◽  
Melvin M. Sweet
Keyword(s):  
Power Series ◽  
Continued Fractions ◽  
Characteristic 2 ◽  
Algebraic Power Series
Sign in / Sign up

Export Citation Format

Share Document