Restricted divisor functions and half Appell sums in higher level
Abstract
We examine the value distributions of coefficients in certain q-series related to half Appell sums in higher level and the first moment of the Garvan’s k-rank of partitions. We prove that these coefficients equal certain restricted divisor functions and can take any nonnegative integer value infinitely many times. As applications, we confirm a conjecture of Xiong on the coefficients of a half Lerch sum and a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of spt-crank-type partitions.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Advanced Mathematical Theories
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 22
- Issue
- 07
- Pages
- 1601–1615
- Publication date
- 17 April 2026
- Language
- EN