On the infinite products derived from theta series I

Daeyeoul Kim; Ja Kyung Koo

doi:10.4134/JKMS.2007.44.1.055

On the infinite products derived from theta series I

Daeyeoul Kim^*
, Ja Kyung Koo

^*Corresponding author for this work

Department of Mathematics

Korea Advanced Institute of Science and Technology

Research output: Contribution to journal › Journal article › peer-review

7 Scopus citations

Abstract

Let k be an imaginary quadratic field, heng the complex upper half plane, and let τ ∈ heng ∩ k, q = e^πiτ. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, ^q1/8/1 + -q/1+q + -q²/1+q² +... ([1]) is transcendental.

Original language	English
Pages (from-to)	55-107
Number of pages	53
Journal	Journal of the Korean Mathematical Society
Volume	44
Issue number	1
DOIs	https://doi.org/10.4134/JKMS.2007.44.1.055
State	Published - 2007.01

Keywords

Algebraic number
Rogers-Ramanujan identities
Theta series
Transcendental number

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.4134/JKMS.2007.44.1.055

Cite this

@article{c49ffd451fb14628af067192227c5dce,

title = "On the infinite products derived from theta series I",

abstract = "Let k be an imaginary quadratic field, heng the complex upper half plane, and let τ ∈ heng ∩ k, q = eπiτ. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, q1/8/1 + -q/1+q + -q2/1+q2 +... ([1]) is transcendental.",

keywords = "Algebraic number, Rogers-Ramanujan identities, Theta series, Transcendental number",

author = "Daeyeoul Kim and Koo, \{Ja Kyung\}",

year = "2007",

month = jan,

doi = "10.4134/JKMS.2007.44.1.055",

language = "English",

volume = "44",

pages = "55--107",

journal = "Journal of the Korean Mathematical Society",

issn = "0304-9914",

number = "1",

}

TY - JOUR

T1 - On the infinite products derived from theta series I

AU - Kim, Daeyeoul

AU - Koo, Ja Kyung

PY - 2007/1

Y1 - 2007/1

N2 - Let k be an imaginary quadratic field, heng the complex upper half plane, and let τ ∈ heng ∩ k, q = eπiτ. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, q1/8/1 + -q/1+q + -q2/1+q2 +... ([1]) is transcendental.

AB - Let k be an imaginary quadratic field, heng the complex upper half plane, and let τ ∈ heng ∩ k, q = eπiτ. In this article, we obtain algebraic numbers from the 130 identities of Rogers-Ramanujan continued fractions investigated in [28] and [29] by using Berndt's idea ([3]). Using this, we get special transcendental numbers. For example, q1/8/1 + -q/1+q + -q2/1+q2 +... ([1]) is transcendental.

KW - Algebraic number

KW - Rogers-Ramanujan identities

KW - Theta series

KW - Transcendental number

UR - https://www.scopus.com/pages/publications/33846222801

U2 - 10.4134/JKMS.2007.44.1.055

DO - 10.4134/JKMS.2007.44.1.055

M3 - Journal article

AN - SCOPUS:33846222801

SN - 0304-9914

VL - 44

SP - 55

EP - 107

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 1

ER -

On the infinite products derived from theta series I

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

Other files and links

Fingerprint

Cite this