Multiplicative $q$-hypergeometric series arising from real quadratic fields

Supercongruences arising from hypergeometric series identities

By using some hypergeometric series identities, we prove two supercongruences on truncated hypergeometric series, one of which is related to a modular Calabi--Yau threefold, and the other is regarded as $p$-adic analogue of an identity due to Ramanujan.

New $q$-supercongruences arising from a summation of basic hypergeometric series

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we find some new $q$-supercongruences. Especially, we give a $q$-analogue of a formula due to Liu [J. Math. Anal. Appl. 497 (2021), Art.~124915].

由一个 ${}_7F_6$ 超几何变换公式产生的超同余式

Supercongruences arising from a ${}_7F_6$ hypergeometric transformation formula

本文借助 ${}_7F_6$ 超几何变换公式证明两个超同余式，其中之一证实 Guo–Liu–Schlosser 猜想并推广 Long–Ramakrishna 的结果。

Hypergeometric identities arising from the elephant random walk

A probabilistic approach is provided to establish new hypergeometric identities. It is based on the calculation of moments of the limiting distribution of the position of the elephant random walk in the superdiffusive regime.

乘法丢番图逼近与晶格和的界

Multiplicative Diophantine approximation and bounds for lattice sums

本文研究晶格和的估计方法，结合整数点计数问题，探讨乘法丢番图逼近的应用与界值。

Multilateral transformations of q-series with quotients of parameters that are nonnegative integer powers of q

We give multidimensional generalizations of several transformation formulae for basic hypergeometric series of a specific type. Most of the upper parameters of the series differ multiplicatively from corresponding lower parameters by a nonnegative integer power of the base q. In one dimension, formulae for such series have been found, in the q -> 1 case, by B. M. Minton and P. W. Karlsson, and in the basic case by G. Gasper, by W. C. Chu, and more recently by the author. Our identities involve multilateral basic hypergeometric series associated to the root system A_r (or equivalently, the unit…