论文标题
在涉及订单2的谐波数的超级企业上
On the supercongruences involving harmonic numbers of order 2
论文作者
论文摘要
我们证明了几个涉及订单的谐波数的超级企业，两个$ h_n^{（2）}：= \ sum_ {k = 1}^n1/k^2 $。例如，如果$ p> 5 $是PRIME，而$α$是$ P $ - 综合，那么我们可以完全确定$$ \ sum_ {k = 0}^{p-1} \ frac {h_k^{（2）}} {k} \ cdot \binomα{k} \ binom {-1-α} {-1-α} {k} {k} \ quad \ quad \ text {and} {and} \ quad \ sum_ {k = 0}^{\ frac {p-1} {2}} \ frac {h_k^{（2）}} {k} {k} \ cdot \ cdot \binomα{k} {k} {k} \ binom {-1-α} {-1-α} {k} $$ modulo $ p^3 $ p^3 $。特别是，通过设置$α= -1/2 $，我们确认了Z.-W的两个猜想一致性。太阳。
We prove several supercongruences involving the harmonic number of order two $H_n^{(2)}:=\sum_{k=1}^n1/k^2$. For example, if $p>5$ is prime and $α$ is $p$-integral, then we can completely determine $$ \sum_{k=0}^{p-1}\frac{H_k^{(2)}}{k}\cdot\binomα{k}\binom{-1-α}{k}\quad\text{and}\quad \sum_{k=0}^{\frac{p-1}{2}}\frac{H_k^{(2)}}{k}\cdot\binomα{k}\binom{-1-α}{k} $$ modulo $p^3$. In particular, by setting $α=-1/2$, we confirm two conjectured congruences of Z.-W. Sun.
