# Arithmetic properties of the partition function

@article{Ahlgren2003ArithmeticPO,
title={Arithmetic properties of the partition function},
author={Scott Ahlgren and Matthew Boylan},
journal={Inventiones mathematicae},
year={2003},
volume={153},
pages={487-502}
}
• Published 10 April 2003
• Mathematics
• Inventiones mathematicae
Let p(n) denote the number of partitions of the positive integer n; p(n) is the number of representations of n as a non-increasing sequence of positive integers (by convention, we agree that p(0) = 1 and that p(n) = 0 if n < 0). The study of the arithmetic properties of p(n) has a long and rich history; see, for example, the works of Andrews, Atkin, Dyson, Garvan, Kim, Stanton, and Swinnerton-Dyer [An,An-G,At1,At-SwD,D,G-K-S]. These works have their origins in the groundbreaking observations of…
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