Huimin Zheng

Three truncated supercongruences for an Apéry-like sequence

For G_n = sum_{k=0}^n 4^k binom(2n-2k,n-k)^2 binom(2k,k), this preprint proves all six cases of a conjecture of Z.-H. Sun concerning three truncated sums with denominators (-16)^n, 8^n, and 32^n modulo p^2. An exact finite-tail transformation reduces the problem to classical trun...

A formal-group proof of a conjecture of Z.-H. Sun for an Apéry-like sequence

Let G_n = sum_{k=0}^n 4^k binom(2n-2k,n-k)^2 binom(2k,k). This preprint proves a conjecture of Z.-H. Sun asserting a three-term congruence for G_{(mp^r-1)/2} when p is congruent to 1 modulo 4. After an integral strict change of parameter, the formal logarithm becomes the Eichler...