Zobrazeno 1 - 10
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pro vyhledávání: '"P. Lasjaunias"'
Autor:
Lasjaunias, Alain
This note is a complement to an article which was published, six years ago, in The Ramanujan Journal (vol. 45.3, 2018). Here, the goal is to fully describe a singular transcendental continued fraction in Q((T^-1)), tied to a particular infinite two l
Externí odkaz:
http://arxiv.org/abs/2409.20233
Autor:
Lasjaunias, Alain, Tran, Jean-Paul
This short note is a comment on a historical aspect of a famous formula dating from the 18th century.
Externí odkaz:
http://arxiv.org/abs/2312.02245
Autor:
Lasjaunias, Alain
By replacing the letters to polynomials in F_2[t], an infinite word, over a finite alphabet, can be seen as the sequence of partial quotients of a continued fraction in F_2((1/t)). Here is described a family of such infinite words, corresponding to c
Externí odkaz:
http://arxiv.org/abs/2212.00516
Autor:
Hu, Yining, Lasjaunias, Alain
Considering an arbitrary pair of distinct and non constant polynomials, $a$ and $b$ in $\mathbb{F}_2[t]$, we build a continued fraction in $\mathbb{F}_2((1/t))$ whose partial quotients are only equal to $a$ or $b$. In a previous work of the first aut
Externí odkaz:
http://arxiv.org/abs/2204.01068
Autor:
Lasjaunias, Alain
In different areas of discrete mathematics, a certain type of polynomials, having coefficients in a field K of finite characteristic, has been considered. The form and the degree of these polynomials, here called projective, are simply linked to the
Externí odkaz:
http://arxiv.org/abs/1910.02648
Autor:
Lasjaunias, Alain
We discuss the form of certain algebraic continued fractions in the field of power series over $F_p$, where p is an odd prime number. This leads to give explicit continued fractions in these fields, satisfying an explicit algebraic equation of arbitr
Externí odkaz:
http://arxiv.org/abs/1803.01739
Autor:
Lasjaunias, Alain
We present a general introduction to continued fractions, with special consideration to the function fields case. These notes were prepared for a summer class given this year in Beijing at Beihang university.
Externí odkaz:
http://arxiv.org/abs/1711.11276
Autor:
Lasjaunias, Alain
Given an odd prime number p, we describe a continued fraction in the field F(p) of power series in 1/T with coefficients in the finite field F_p, where T is a formal indeterminate. This continued fraction satisfies an algebraic equation of a particul
Externí odkaz:
http://arxiv.org/abs/1710.00613
Autor:
Lasjaunias, Alain
The goal of this survey paper is to present, in chronological order, certain research works on continued fractions in power series fields over a finite field, all of them being derivated from some examples introduced thirty years ago by Mills and Rob
Externí odkaz:
http://arxiv.org/abs/1704.08959
We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a generating function of a particular sequence in the set {1, 2}. The origi
Externí odkaz:
http://arxiv.org/abs/1607.07235