Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.04801 |
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Sommario:
- Let $q$ be a Pisot or Salem number. Let $f_j(x)$ $(j=1,2,\dots)$ be integer-valued polynomials of degree $\ge2$ with positive leading coefficients, and let $\{a_j (n)\}_{n\ge1}$ $(j=1,2,\dots)$ be sequences of algebraic integers in the field $\mathbb{Q}(q)$ with suitable growth conditions. In this paper, we investigate linear independence over $\mathbb{Q}(q)$ of the numbers \begin{equation*} 1,\qquad \sum_{n=1}^{\infty} \frac{a_j (n)}{q^{f_j (n)}} \quad (j=1,2,\dots). \end{equation*} In particular, when $a_j(n)$ $(j=1,2,\dots)$ are polynomials of $n$, we give a linear independence criterion for the above numbers.