Proofs of conjectures of Chan for \(d(n)\) (Q2111893)

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.