Congruences for Taylor expansions of quantum modular forms - Kölner UniversitätsPublikationsServer

Guerzhoy, Pavel, Kent, Zachary A. and Rolen, Larry ORCID: 0000-0001-8671-8117 (2014). Congruences for Taylor expansions of quantum modular forms. Res. Math. Sci., 1 (1). CHAM: SPRINGER INTERNATIONAL PUBLISHING AG. ISSN 2197-9847

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DOI:10.1186/s40687-014-0017-2

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.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Guerzhoy, Pavel	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Kent, Zachary A.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Rolen, Larry	UNSPECIFIED	orcid.org/0000-0001-8671-8117	UNSPECIFIED