按代数数的幂分区

The Ramanujan Journal Pub Date : 2024-04-17 DOI:10.1007/s11139-024-00845-2

Vítězslav Kala, Mikuláš Zindulka

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引用次数: 0

摘要

我们研究复数的分区作为一个固定代数数 \(\beta \)的非负幂之和。我们证明，如果\(\beta \)是实二次数，那么当且仅当\(\beta \)的某个共轭大于1时，分区的数目总是有限的。此外，我们还证明，对于满足一定条件的\(\beta \)，分区函数的值都是非负整数。

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Partitions into powers of an algebraic number

We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number \(\beta \). We prove that if \( \beta \) is real quadratic, then the number of partitions is always finite if and only if some conjugate of \(\beta \) is larger than 1. Further, we show that for \(\beta \) satisfying a certain condition, the partition function attains all non-negative integers as values.

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The Ramanujan Journal

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