Asymptotics of certain double series in Eulerian form

Byungchan Kim; Eunmi Kim

doi:10.1142/S1793042119500544

Asymptotics of certain double series in Eulerian form

Byungchan Kim
, Eunmi Kim

School of Natural Sciences

Korea Institute for Advanced Study

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

Abstract

We examine the asymptotic behavior of FA,B(q) := Pn=(r s)tZ2 =0 q 12 ntAn+Bn (q)r(q)s where A = a1 a2 a2 a1, B = (b1 b2), and a1, a2, b1, b2 are rational numbers satisfying some conditions while ntAn is not necessarily positive-definite. As an application, we obtain non-modularities of certain double-sum Eulerian series.

Original language	English
Pages (from-to)	1009-1021
Number of pages	13
Journal	International Journal of Number Theory
Volume	15
Issue number	5
DOIs	https://doi.org/10.1142/S1793042119500544
State	Published - 1 Jun 2019

Keywords

asymptotic formula
double-sum Eulerian series
Modularity
q-series

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abstract = "We examine the asymptotic behavior of FA,B(q) := Pn=(r s)tZ2 =0 q 12 ntAn+Bn (q)r(q)s where A = a1 a2 a2 a1, B = (b1 b2), and a1, a2, b1, b2 are rational numbers satisfying some conditions while ntAn is not necessarily positive-definite. As an application, we obtain non-modularities of certain double-sum Eulerian series.",

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AB - We examine the asymptotic behavior of FA,B(q) := Pn=(r s)tZ2 =0 q 12 ntAn+Bn (q)r(q)s where A = a1 a2 a2 a1, B = (b1 b2), and a1, a2, b1, b2 are rational numbers satisfying some conditions while ntAn is not necessarily positive-definite. As an application, we obtain non-modularities of certain double-sum Eulerian series.

KW - asymptotic formula

KW - double-sum Eulerian series

KW - Modularity

KW - q-series

UR - https://www.scopus.com/pages/publications/85060028397

U2 - 10.1142/S1793042119500544

DO - 10.1142/S1793042119500544

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SP - 1009

EP - 1021

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 5

ER -

Asymptotics of certain double series in Eulerian form

Abstract

Keywords

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