3 papers
math.NT2020
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…
math.NT2019
Linear independence results for certain sums of reciprocals of Fibonacci and Lucas numbers
Daniel Duverney, Yuta Suzuki, Yohei Tachiya
The aim of this paper is to give linear independence results for the values of certain series. As an application, we derive arithmetical properties of the sums of reciprocals of Fi…
math.NT2016
Algebraic independence results for values of Theta-constants, II
Carsten Elsner, Yohei Tachiya
Let with denote the Thetanullwert of the Jacobi theta function \[θ(z|τ) \,=\,\sum_{ν=-\infty}^{\infty} e^{πiν^2τ+ 2πiνz} \,.\] M…