On some double-sum false theta series

Song Heng Chan; Byungchan Kim

doi:10.1016/j.jnt.2018.02.012

On some double-sum false theta series

Song Heng Chan, Byungchan Kim

School of Natural Sciences

Nanyang Technological University

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

4 Scopus citations

Abstract

We compute false theta series obtained from the double-sum g_a,b,c(x,y,q)=(∑r,s≥0+∑r,s<0)(−1)^r+sx^ry^sq^{a(r2)+brs+c(s2)}. We investigate its number-theoretic and combinatorial implications using q-series and unimodal sequences.

Original language	English
Pages (from-to)	40-55
Number of pages	16
Journal	Journal of Number Theory
Volume	190
DOIs	https://doi.org/10.1016/j.jnt.2018.02.012
State	Published - Sep 2018

Keywords

Bailey Lemma
Bailey pairs
Double-sum false theta series
False theta series
Unimodal sequences

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10.1016/j.jnt.2018.02.012

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title = "On some double-sum false theta series",

abstract = "We compute false theta series obtained from the double-sum ga,b,c(x,y,q)=(∑r,s≥0+∑r,s<0)(−1)r+sxrysqa(r2)+brs+c(s2). We investigate its number-theoretic and combinatorial implications using q-series and unimodal sequences.",

keywords = "Bailey Lemma, Bailey pairs, Double-sum false theta series, False theta series, Unimodal sequences",

author = "Chan, {Song Heng} and Byungchan Kim",

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AU - Kim, Byungchan

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N2 - We compute false theta series obtained from the double-sum ga,b,c(x,y,q)=(∑r,s≥0+∑r,s<0)(−1)r+sxrysqa(r2)+brs+c(s2). We investigate its number-theoretic and combinatorial implications using q-series and unimodal sequences.

AB - We compute false theta series obtained from the double-sum ga,b,c(x,y,q)=(∑r,s≥0+∑r,s<0)(−1)r+sxrysqa(r2)+brs+c(s2). We investigate its number-theoretic and combinatorial implications using q-series and unimodal sequences.

KW - Bailey Lemma

KW - Bailey pairs

KW - Double-sum false theta series

KW - False theta series

KW - Unimodal sequences

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DO - 10.1016/j.jnt.2018.02.012

M3 - Article

AN - SCOPUS:85044330184

SN - 0022-314X

VL - 190

SP - 40

EP - 55

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

On some double-sum false theta series

Abstract

Keywords

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