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arXiv · 2203.11786

Algebraic degree of series of reciprocal algebraic integers

Mathias Løkkegaard Laursen
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Abstract

In this paper, I give sufficient conditions for any linear combination in $\mathbb{Q}$ of numbers $\sum_{n=1}^{\infty}\frac{b_{1,n}}{\alpha_{1,n}}$, $\ldots$, $\sum_{n=1}^{\infty}\frac{b_{K,n}}{\alpha_{K,n}}$ 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.

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Mathias Løkkegaard Laursen. 2022-03-22. Algebraic degree of series of reciprocal algebraic integers. https://doi.org/10.1216/rmj.2023.53.517

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