scholarly journals Fast coefficient computation for algebraic power series in positive characteristic

2019 ◽  
Vol 2 (1) ◽  
pp. 119-135 ◽  
Author(s):  
Alin Bostan ◽  
Xavier Caruso ◽  
Gilles Christol ◽  
Philippe Dumas
Keyword(s):  
Power Series ◽  
Positive Characteristic ◽  
Algebraic Power Series

scholarly journals Continued fractions and diophantine equations in positive characteristic

2021 ◽  
Vol 109 (123) ◽  
pp. 143-151
Author(s):  
Khalil Ayadi ◽  
Awatef Azaza ◽  
Salah Beldi
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Diophantine Equations ◽  
Positive Characteristic ◽  
Continued Fraction Expansion ◽  
Ring Of Polynomials ◽  
Algebraic Power Series

We exhibit explicitly the continued fraction expansion of some algebraic power series over a finite field. We also discuss some Diophantine equations on the ring of polynomials, which are intimately related to these power series.

Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic

2013 ◽  
Vol 56 (4) ◽  
pp. 673-683
Author(s):  
K. Ayadi ◽  
M. Hbaib ◽  
F. Mahjoub
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Diophantine Approximation ◽  
Positive Characteristic ◽  
Rational Approximations ◽  
Positive Degree ◽  
Formal Power ◽  
Algebraic Power Series

Abstract.In this paper, we study rational approximations for certain algebraic power series over a finite field. We obtain results for irrational elements of strictly positive degree satisfying an equation of the typewhere (A, B, C) ∊ (𝔽q[X])2 × 𝔽*q [X]. In particular, under some conditions on the polynomials A, B and C, we will give well approximated elements satisfying this equation.

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
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