Hao Pan

activity

20042026

most cited

p

-adic analogues of hypergeometric identities

11 citations · 115 across the 90 of their papers we have counts for

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Showing 2019Show all

4 papers · 1 filter

math.NT2019

A local-global theorem for $p$ -adic supercongruences

Hao Pan, Roberto Tauraso, Chen Wang

Let $Z_{p}$ denote the ring of all $p$ -adic integers and call $U = {(x_{1}, \dots, x_{n}) : a_{1} x_{1} + \dots + a_{n} x_{n} + b = 0}$ a hyperplane over $Z_{p}^{n}$ , where at…

math.CO2019

A new trigonometric identity with applications

Zhi-Wei Sun, Hao Pan

In this paper we obtain a new curious identity involving trigonometric functions. Namely, for any positive odd integer $n$ we prove that $$\sum_{k=1}^n(-1)^k(\cot kx)\sin k(n-k)x=\…

math.CO2019

A $q$ -analogue of Wilson's congruence

Hao Pan, Yu-Chen Sun

Let $C_{n}$ be the set of all permutation cycles of length $n$ over ${1, 2, \dots, n}$ . Let $f_{n} (q) := σ \in C_{n + 1} \sum q^{m aj σ}$ be a…

math.NT2019★ 2 cited

The Green-Tao theorem for Piatetski-Shapiro primes

Hongze Li, Hao Pan

Let $m \geq 3$ . Suppose that $1 - 2^{- 2^{m^{2} 4^{m}}} < γ < 1.$ Then the set ${p prime : p = [n^{\frac{1}{γ}}] for some n \in N}$ contains infinitely many non-trivi…

A local-global theorem for p-adic supercongruences

A new trigonometric identity with applications

A q-analogue of Wilson's congruence

The Green-Tao theorem for Piatetski-Shapiro primes

A local-global theorem for $p$ -adic supercongruences

A $q$ -analogue of Wilson's congruence