author = {Koustav Banerjee and Peter Paule and Cristian-Silviu Radu and Carsten Schneider},
title = {{Asymptotics for the reciprocal and shifted quotient of the partition function}},
language = {english},
abstract = {Let $p(n)$ denote the partition function. In this paper our main goal is to derive an asymptotic expansion up to order $N$ (for any fixed positive integer $N$) along with estimates for error bounds for the shifted quotient of the partition function, namely $p(n+k)/p(n)$ with $kin mathbb{N}$, which generalizes a result of Gomez, Males, and Rolen. In order to do so, we derive asymptotic expansions with error bounds for the shifted version $p(n+k)$ and the multiplicative inverse $1/p(n)$, which is of independent interest. },
journal = {Research in Number Theory},
volume = {11},
number = {101},
pages = {1--46},
isbn_issn = {ISSN 2363-9555},
year = {2025},
note = { arXiv:2412.02257 [math.NT]},
refereed = {yes},
length = {46},
url = {https://doi.org/10.1007/s40993-025-00678-y}