C. Elsner

collaborators

3 papers

math.NT2018

On linear relations for Dirichlet series formed by recursive sequences of second order

Carsten Elsner, Niclas Technau

Let $F_{n}$ and $L_{n}$ be the Fibonacci and Lucas numbers, respectively. Four corresponding zeta functions in $s$ are defined by \[ζ_F(s) \,:=\, \sum_{n=1}^{\infty} \frac{1}{F_n^s}\,,…

math.NT2016

Algebraic independence results for values of Theta-constants, II

Carsten Elsner, Yohei Tachiya

Let $θ_{3} (τ) = 1 + 2 \sum_{ν = 1}^{\infty} q^{ν^{2}}$ with $q = e^{iπ τ}$ denote the Thetanullwert of the Jacobi theta function \[θ(z|τ) \,=\,\sum_{ν=-\infty}^{\infty} e^{πiν^2τ+ 2πiνz} \,.\] M…

math.NT2016

On error sums formed by rational approximations with split denominators

Thomas Baruchel, Carsten Elsner

In this paper we consider error sums of the form \[\sum_{m=0}^{\infty} \varepsilon_m\Big( \,b_mα- \frac{a_m}{c_m}\,\Big) \,,\] where $α$ is a real number, $a_{m}$ , $b_{m}$ , $c_{m}$ are i…