\(q\)-series and \(L\)-functions related to half-derivatives of the Andrews-Gordon identity

DOI10.1007/S11139-006-6506-1zbMath1114.11039arXivmath/0303250OpenAlexW2008269716MaRDI QIDQ850526

Kazuhiro Hikami

Publication date: 3 November 2006

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0303250

zbMATH Keywords

quantum invariantsAndrews-Gordon identitiestorus knotL-functionscolored Jones polynomial

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Relations with algebraic geometry and topology (11F23)

Related Items (22)

DAHA-Jones polynomials of torus knots ⋮ Quantum modularity of partial theta series with periodic coefficients ⋮ Torus knots and quantum modular forms ⋮ Asymptotics of the colored Jones polynomial and the A-polynomial ⋮ Congruences for Taylor expansions of quantum modular forms ⋮ Volume Conjecture and Asymptotic Expansion ofq-Series ⋮ A ``strange vector-valued quantum modular form ⋮ Periodic partial theta functions and \(q\)-hypergeometric knot multisums as quantum Jacobi forms ⋮ Asymptotics and sign patterns for coefficients in expansions of Habiro elements ⋮ Half-integral weight Eichler integrals and quantum modular forms ⋮ Resurgence analysis of quantum invariants of Seifert fibered homology spheres ⋮ Generalized Fishburn numbers and torus knots ⋮ Asymptotics and statistics on Fishburn matrices and their generalizations ⋮ COLORED JONES POLYNOMIALS WITH POLYNOMIAL GROWTH ⋮ A framework of Rogers-Ramanujan identities and their arithmetic properties ⋮ Unnamed Item ⋮ On the quantum invariants for the spherical Seifert manifolds ⋮ Dissections of strange \(q\)-series ⋮ On sum-of-tails identities ⋮ Quantum Jacobi forms in number theory, topology, and mathematical physics ⋮ The colored Jones polynomial and Kontsevich–Zagier series for double twist knots ⋮ Congruences and relations for \(r\)-Fishburn numbers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modular forms and quantum invariants of \(3\)-manifolds
• \(q\)-series identities and values of certain \(L\)-functions
• A LINK INVARIANT FROM QUANTUM DILOGARITHM
• A $q$-series identity and the arithmetic of Hurwitz zeta functions
• Volume Conjecture and Asymptotic Expansion ofq-Series
• Hypergeometric generating functions for values of Dirichlet and other L functions
• The colored Jones polynomials and the simplicial volume of a knot
• The concept of Bailey chains
• Vassiliev invariants and a strange identity related to the Dedekind eta-function

This page was built for publication: \(q\)-series and \(L\)-functions related to half-derivatives of the Andrews-Gordon identity