Odd-balanced unimodal sequences and related functions: Parity, mock modularity and quantum modularity

Byungchan Kim; Subong Lim; Jeremy Lovejoy

doi:10.1090/proc/13027

Odd-balanced unimodal sequences and related functions: Parity, mock modularity and quantum modularity

Byungchan Kim
, Subong Lim
, Jeremy Lovejoy

School of Natural Sciences

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

15 Scopus citations

Abstract

We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo 2 and 4. We also study two related functions which share some of the properties of U(x, q) and V(x, q).

Original language	English
Pages (from-to)	3687-3700
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	9
DOIs	https://doi.org/10.1090/proc/13027
State	Published - 2016

Keywords

Congruences
Mock theta functions
Quantum modular forms
Rank
Unimodal sequences

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10.1090/proc/13027

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abstract = "We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo 2 and 4. We also study two related functions which share some of the properties of U(x, q) and V(x, q).",

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AU - Lovejoy, Jeremy

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N2 - We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo 2 and 4. We also study two related functions which share some of the properties of U(x, q) and V(x, q).

AB - We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo 2 and 4. We also study two related functions which share some of the properties of U(x, q) and V(x, q).

KW - Congruences

KW - Mock theta functions

KW - Quantum modular forms

KW - Rank

KW - Unimodal sequences

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DO - 10.1090/proc/13027

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ER -

Odd-balanced unimodal sequences and related functions: Parity, mock modularity and quantum modularity

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Keywords

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