Algebraic degree of series of reciprocal algebraic integers

Abstract

In this paper, I give sufficient conditions for any linear combination in $\mathbb{Q}$ of numbers ${\sum }_{n=1}^{\infty }\frac{b_{1,n}}{{\alpha }_{1,n}}$, $\dots$, ${\sum }_{n=1}^{\infty }\frac{b_{K,n}}{{\alpha }_{K,n}}$ to have algebraic degree greater than an arbitrary fixed integer $D$ when the numbers ${\alpha }_{i,n}$ are algebraic integers of sufficiently rapidly increasing modulus and the $b_{i,n}$ are positive integers that are not too large.

15 pages

Cited by in corpus (1)

• Transcendence of certain sequences of algebraic numbers