arXiv subjects

Guozhu Ruan

Publications and source records attributed to Guozhu Ruan.

3 recordsLinked to original sources

arXiv2026

Two parametric q-supercongruences from a summation formula for q-series

With the help of a summation formula for $q$-series and the creative microscoping method, we shall establish two parametric $q$-supercongruences. They are both modulo the third power of a cyclotomic polynomial. When $q\to1$, one of them is able to engender the following conclusion: for any prime $p\equiv2\pmod{3}$ and any nonnegative integer $s$ subject to $ s\leq (p-2)/3$, \[\sum_{k=s}^{(p+1)/3+s}(6k-1)\frac{(-\frac{1}{3})_{k-s}(-\frac{1}{3})_{k+s}(-\frac{1}{3})_{k}}{(k-s)!(k+s)!k!} \equiv 0\pmod{p^3}.\]

math.CO↗

arXiv2024

Multidimensional Rogers-Ramanujan type identities with parameters

Via the contour integral method, we establish a reduction formula from a double series to a single series with parameters, which not only implies Uncu and Zudilin's two results and Cao and Wang's two results, but also is related to Berkovich and Warnaar's equation. Similarly, we also discover some triple-sum generalizations of Cao and Wang's formulas. As conclusions, several multidimensional Rogers--Ramanujan type identities with parameters or without parameters are given.

math.CO↗

arXiv2022

Double series for $π$ and their $q$-analogues

With the help of the partial derivative operator and several summation formulas for hypergeometric series, we find three double series for $π$. In terms of the operator just stated and several summation formulas for basic hypergeometric series, we also establish $q$-analogues of these double series.

math.CO↗