q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
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DOI：
10.1142/s1793042119501069
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发表时间：
2019-10-01
影响因子：
0.7
通讯作者：
Gorodetsky, Ofir
中科院分区：
文献类型：
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作者：
Gorodetsky, Ofir
通过证明相应的 q-超同余，我们建立了 Almkvist 和 Zudilin 猜想的超同余。通过涉及单位根处的更高导数的一般标准，为二项式系数和 Apery 数建立了类似的 q-超同余。我们的方法使我们发现了涉及 q-卢卡斯数的循环筛分现象的新例子。
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding q-supercongruence. Similar q-supercongruences are established for binomial coefficients and the Apery numbers, by means of a general criterion involving higher derivatives at roots of unity. Our methods lead us to discover new examples of the cyclic sieving phenomenon, involving the q-Lucas numbers.