Ankush Goswami,
"Congruences for generalized Fishburn numbers at roots of unity"
, Serie RISC Report Series, Nummer 20-09, RISC, JKU, Hagenberg, Linz, 2020
Original Titel:
Congruences for generalized Fishburn numbers at roots of unity
Sprache des Titels:
Englisch
Original Kurzfassung:
There has been significant recent interest in the arithmetic properties of the coefficients of $F(1-q)$ and $\mathcal{F}_t(1-q)$ where $F(q)$ is the Kontsevich-Zagier strange series and $\mathcal{F}_t(q)$ 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 $(\zeta_N - q)^s F((\zeta_N - q)^r)$ and $(\zeta_N - q)^s \mathcal{F}_t((\zeta_N - q)^r)$, where $\zeta_N$ is an $N$th root of unity and $r$, $s$ are certain integers.