10 citations · 11 across the 17 of their papers we have counts for
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Note on sums involving the Euler function
Shane Chern
In this note, we provide refined estimates of the following sums involving the Euler totient function: $$\sum_{n\le x} ϕ\left(\left[\frac{x}{n}\right]\right) \qquad \text{and} \qqu…
Linked partition ideals and Kanade--Russell conjectures
Shane Chern, Zhitai Li
This paper will primarily present a method of proving generating function identities for partitions from linked partition ideals. The method we introduce is built on a conjecture b…
A further look at the truncated pentagonal number theorem
Shane Chern
In this paper, we study the asymptotic behavior of the following function which arises from Andrew…
Elementary proof of congruences modulo 25 for broken -diamond partitions
Shane Chern, Dazhao Tang
Let denote the number of -broken diamond partitions of . Quite recently, the second author proved an infinite family of congruences modulo 25 for with t…
Asymptotics for the Fourier coefficients of eta-quotients
Shane Chern
We study the asymptotics for the Fourier coefficients of a broad class of eta-quotients, where $m_1,\ld…
Some inequalities for Garvan's bicrank function of 2-colored partitions
Shane Chern, Dazhao Tang, Liuquan Wang
In order to provide a unified combinatorial interpretation of congruences modulo for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted v…