1 citations · 1 across the 8 of their papers we have counts for
8 papers
Stern polynomials and algebraic independence
Daniel Duverney, Iekata Shiokawa
Let and be integers. Let with be the limit of a certain subsequence of the Stern polynomials introduced by Dilcher and Eri…
Continuants and convergence of certain continued fractions
Daniel Duverney, Iekata Shiokawa
We give a concise introduction to the theory of continuants and show how Perron used them in his proof of Tietze theorem on the convergence of infinite semi-regular continued fract…
A new proof of a theorem of Tietze
Daniel Duverney, Iekata Shiokawa
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
Irrationality exponents of semi-regular continued fractions
Daniel Duverney, Iekata Shiokawa
We prove that the formula giving the exact value of the irrationality exponent of regular continued fractions remains valid for semi-regular continued fractions satisfyiong certain…
Algebraic independence of certain infinite products involving the Fibonacci numbers
Daniel Duverney, Yohei Tachiya
Let be the sequence of the Fibonacci numbers. The aim of this paper is to give explicit formulae for the infinite products \[ \prod_{n=1}^{\infty}\left( 1+\fra…
Irrationality exponents of generalized Hone series
Daniel Duverney, Takeshi Kurosawa, Iekata Shiokawa
We compute the exact irrationality exponents of certain series of rational numbers, first studied in a special case by Hone, by transforming them into suitable continued fractions.