4 papers
Transformation Formulae and Applications for Double Lambert Series
Rong Chen, Tianjian Xu
In this paper, we study a class of double Lambert series and establish several identities and transformation relations for them. These formulae provide useful tools for reducing ce…
A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture
Rong Chen, Tianjian Xu
In this paper, we prove a generalization of a conjecture of Amdeberhan, Andrews, and Ballantine on double Lambert series. Motivated by a question raised by Cui, Kumar, and Singh co…
On Bilateral Multiple Sums and Rogers-Ramanujan Type Identities
Dandan Chen, Tianjian Xu
We establish some new bilateral double-sum Rogers-Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers-Ramanujan type ide…
Congruences modulo powers of for -elongated plane partitions
Dandan Chen, Tianjian Xu, Siyu Yin
The enumeration of -elongated plane partition diamonds has emerged as a generalization of the classical integer partition function . Congruences for modu…