Asymptotics and sign patterns for coefficients in expansions of Habiro elements

DOI10.1007/s00209-023-03307-5arXiv2204.02628MaRDI QIDQ6115072

Abhash Kumar Jha, Byungchan Kim, Ankush Goswami, Robert Osburn

Publication date: 12 July 2023

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.02628

zbMATH Keywords

asymptoticsHabiro ringgeneralized Fishburn numbersstrange identities

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Asymptotic enumeration (05A16) Special sequences and polynomials (11B83) (q)-gamma functions, (q)-beta functions and integrals (33D05) Completion of commutative rings (13B35) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16)

Cites Work

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• Cyclotomic completions of polynomial rings
• \(q\)-series and \(L\)-functions related to half-derivatives of the Andrews-Gordon identity
• Congruences for the Fishburn numbers
• Combinatorial proofs of identities in Ramanujan's lost notebook associated with the Rogers-Fine identity and false theta functions
• Quantum modularity of partial theta series with periodic coefficients
• Generalized Fishburn numbers and torus knots
• Dissections of strange \(q\)-series
• Congruences and relations for \(r\)-Fishburn numbers
• Dissections of a "strange" function
• Congruences for Fishburn numbers modulo prime powers
• An Introduction to Ramanujan's "lost" Notebook
• ENUMERATION OF CHORD DIAGRAMS AND AN UPPER BOUND FOR VASSILIEV INVARIANTS
• Congruences for generalized Fishburn numbers at roots of unity
• Vassiliev invariants and a strange identity related to the Dedekind eta-function

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