Proofs of conjectures of Chan for \(d(n)\)
type: Item
instance of: scholarly article
title: Proofs of conjectures of Chan for \(d(n)\)
author: Su-Ping Cui
published in: The Ramanujan Journal
publication date: 2023-01-17T00:00:00Z
review text: The author proves some congruences for the coefficients of a function related to Ramanujan's sixth order mock theta function \(\phi(q)\), with the help of a result developed by \textit{S. H. Chan} [Acta Arith. 153, No. 2, 161--189 (2012; Zbl 1264.11089)]. Theorem \(1.3\), which is one special case of Entry \(6.3.7\) in Ramanujan's lost note book Part II, has been proved using work done by \textit{R. P. Agarwal} [J. Math. Phys. Sci. 18, 291--322 (1984; Zbl 0593.65097)]. Further, Theorem \(1.4\) is proved by using the results of Theorem \(1.3\), and Theorem \(1.5\) is proved by using the results of Theorem \(1.4\). All the results presented in this article are explained properly with supporting arguments.
reviewed by: M. P. Chaudhary
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 7643084
zbMATH Keywords: partial theta function
zbMATH Keywords: mock theta function
zbMATH Keywords: congruence
Wikidata QID: Q115231681
MaRDI profile type: Publication
full work available at URL: s11139-022-00643-8
OpenAlex ID: W4304187445
cites work: The number of smallest parts in the partitions of n
cites work: On the paper ''a 'lost' notebook of Ramanujan''
cites work: Proofs of some conjectures of Chan on Appell-Lerch sums
cites work: Congruences for Ramanujan's φ function
cites work: TWO CONGRUENCES FOR APPELL–LERCH SUMS
cites work: Proof of a conjectural congruence of Chan for Appell–Lerch sums
cites work: Arithmetic properties for Appell-Lerch sums
cites work: Q4040189
cites work: Q4828543
cites work: Q4040264
cites work: Generalizations of some conjectures of Chan on congruences for Appell-Lerch sums
DOI: 10.1007/S11139-022-00643-8
description: scientific article; zbMATH DE number 7643084