Partitions into powers of an algebraic number
Abstract
We study partitions of complex numbers as sums of nonnegative 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 nonnegative integers as values.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.16688
 arXiv:
 arXiv:2305.16688
 Bibcode:
 2023arXiv230516688K
 Keywords:

 Mathematics  Number Theory;
 11P81;
 11P84;
 11R11
 EPrint:
 10 pages, to appear in Ramanujan J