Work

Restricted divisor functions and half Appell sums in higher level

Year: 2026

Type: article

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.

Source: International Journal of Number Theory

DOI: 10.1142/s1793042126500818

Authors: Meng-Juan Tian, Nian Hong Zhou

Institution: Guangxi Normal University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G3379435980