A note on the arithmetic nature of some infinite series (Q2330075)

The paper deals with the several theorems concerning the transcendence and linear independence of the numbers \[ \sum_{n\in\mathbb{Z}} \frac{f(n)}{n^2+\alpha^2} \quad \text{and} \quad \sum_{n\in\mathbb{Z}} \frac{g(n)}{(2n+1+\beta)^a},\] where \(\alpha\) is the special root of the qudratic polynomial, \(\beta\) is a special complex number and \(f(x)\) and \(g(x)\) are special periodic functions. The proofs are in the spirit of Nesterenko.