Photo from archive.org
Recently, Chan and Wang proved numerous congruences satisfied by $$p_{a/b}(n)$$, where $$p_{a/b}(n)$$ denotes the coefficient of $$q^n$$ in the series expansion of $$(q;q)_\infty ^{\frac{a}{b}}$$. Moreover, they presented many conjectures on… Click to show full abstract
Recently, Chan and Wang proved numerous congruences satisfied by $$p_{a/b}(n)$$, where $$p_{a/b}(n)$$ denotes the coefficient of $$q^n$$ in the series expansion of $$(q;q)_\infty ^{\frac{a}{b}}$$. Moreover, they presented many conjectures on the congruences for $$p_{a/b}(n)$$. In this paper, we not only prove some conjectures of Chan and Wang, but also discover new congruences for $$p_{a/b}(n)$$ in light of Ramanujan’s modular equations of fifth, seventh and thirteenth orders.
Journal Title: Ramanujan Journal
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!