论文标题
一致性的统一根源
Congruences for generalized Fishburn numbers at roots of unity
论文作者
论文摘要
最近，人们对$ f（1-q）$和$ \ mathscr {f} _t（1-q）$的系数的算术属性产生了重大兴趣，其中$ f（q）$是kontsevich-zagier奇怪的系列和$ \ $ \ mathscr {f} _t（f} _t（q）奥斯本，拉什沃思，特伦斯加德和周。在本文中，我们证明了两个普通鱼类数量的家族，即$（ζ_n -q）^s f（（（ζ_N -q）^r）$和$（ζ_n -q） $ r $，$ s $是某些整数。
There has been significant recent interest in the arithmetic properties of the coefficients of $F(1-q)$ and $\mathscr{F}_t(1-q)$ where $F(q)$ is the Kontsevich-Zagier strange series and $\mathscr{F}_t(q)$ is the strange series associated to a family of torus knots as studied by Bijaoui, Boden, Myers, Osburn, Rushworth, Tronsgard and Zhou. In this paper, we prove prime power congruences for two families of generalized Fishburn numbers, namely, for the coefficients of $(ζ_N - q)^s F((ζ_N - q)^r)$ and $(ζ_N - q)^s \mathscr{F}_t((ζ_N - q)^r)$, where $ζ_N$ is an $N$th root of unity and $r$, $s$ are certain integers.
