Author:
Guerzhoy Pavel,Kent Zachary A,Rolen Larry
Abstract
Abstract
Recently, a beautiful paper of Andrews and Sellers has established linear congruences for the Fishburn numbers modulo an infinite set of primes. Since then, a number of authors have proven refined results, for example, extending all of these congruences to arbitrary powers of the primes involved. Here, we take a different perspective and explain the general theory of such congruences in the context of an important class of quantum modular forms. As one example, we obtain an infinite series of combinatorial sequences connected to the ‘half-derivatives’ of the Andrews-Gordon functions and with Kashaev’s invariant on (2m+1,2) torus knots, and we prove conditions under which the sequences satisfy linear congruences modulo at least 50% of primes.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Mathematics (miscellaneous),Theoretical Computer Science
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