@**techreport**{RISC6119,author = {Ankush Goswami},

title = {{Congruences for generalized Fishburn numbers at roots of unity}},

language = {english},

abstract = {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.},

number = {20-09},

year = {2020},

length = {17},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}