Partitions into powers of an algebraic number
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2023
- DOI:
- 10.48550/arXiv.2305.16688
- arXiv:
- arXiv:2305.16688
- Bibcode:
- 2023arXiv230516688K
- Keywords:
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- Mathematics - Number Theory;
- 11P81;
- 11P84;
- 11R11
- E-Print:
- 10 pages, to appear in Ramanujan J