Dissections of Strange q-Series

Scott Ahlgren; Byungchan Kim; Jeremy Lovejoy

doi:10.1007/s00026-019-00447-6

Dissections of Strange q-Series

Scott Ahlgren
, Byungchan Kim
, Jeremy Lovejoy

School of Natural Sciences

University of Illinois at Urbana-Champaign
University of California at Berkeley
CNRS

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.

Original language	English
Pages (from-to)	427-442
Number of pages	16
Journal	Annals of Combinatorics
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1007/s00026-019-00447-6
State	Published - 1 Nov 2019

Keywords

Congruences
Fishburn numbers
Kontsevich–Zagier strange function
Partial theta functions
q-Series

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10.1007/s00026-019-00447-6

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title = "Dissections of Strange q-Series",

abstract = "In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.",

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author = "Scott Ahlgren and Byungchan Kim and Jeremy Lovejoy",

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AU - Kim, Byungchan

AU - Lovejoy, Jeremy

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N2 - In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.

AB - In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.

KW - Congruences

KW - Fishburn numbers

KW - Kontsevich–Zagier strange function

KW - Partial theta functions

KW - q-Series

UR - https://www.scopus.com/pages/publications/85074618410

U2 - 10.1007/s00026-019-00447-6

DO - 10.1007/s00026-019-00447-6

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AN - SCOPUS:85074618410

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SP - 427

EP - 442

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 3-4

ER -

Dissections of Strange q-Series

Abstract

Keywords

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