On the infinite products derived from theta series II

Daeyeoul Kim; Ja Kyung Koo

doi:10.4134/JKMS.2008.45.5.1379

On the infinite products derived from theta series II

Daeyeoul Kim^*
, Ja Kyung Koo

^*Corresponding author for this work

Department of Mathematics

National Institute for Mathematical Sciences
Korea Advanced Institute of Science and Technology

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

Abstract

Let k be an imaginary quadratic field, h the complex upper half plane, and let τ ∈ h ∩ k, q = e^πiτ. For n, t ∈ ℤ⁺ with 1 ≤ t ≤ n - 1, set n = z · 2^l (z = 2, 3, 5, 7, 9, 13, 15) with l ≥ 0 integer. Then we show that q ^{n/12-t/2+t2/2n} Π^∞_m=1 (1-q ^nm-t)(1-q^nm-(n-t)) are algebraic numbers.

Original language	English
Pages (from-to)	1379-1391
Number of pages	13
Journal	Journal of the Korean Mathematical Society
Volume	45
Issue number	5
DOIs	https://doi.org/10.4134/JKMS.2008.45.5.1379
State	Published - 2008.09

Keywords

Algebraic number
Rogers-Ramanujan identities
Theta series

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10.4134/JKMS.2008.45.5.1379

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

abstract = "Let k be an imaginary quadratic field, h the complex upper half plane, and let τ ∈ h ∩ k, q = eπiτ. For n, t ∈ ℤ+ with 1 ≤ t ≤ n - 1, set n = z · 2l (z = 2, 3, 5, 7, 9, 13, 15) with l ≥ 0 integer. Then we show that q n/12-t/2+t2/2n Π∞m=1 (1-q nm-t)(1-qnm-(n-t)) are algebraic numbers.",

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

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

year = "2008",

month = sep,

doi = "10.4134/JKMS.2008.45.5.1379",

language = "English",

volume = "45",

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T1 - On the infinite products derived from theta series II

AU - Kim, Daeyeoul

AU - Koo, Ja Kyung

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N2 - Let k be an imaginary quadratic field, h the complex upper half plane, and let τ ∈ h ∩ k, q = eπiτ. For n, t ∈ ℤ+ with 1 ≤ t ≤ n - 1, set n = z · 2l (z = 2, 3, 5, 7, 9, 13, 15) with l ≥ 0 integer. Then we show that q n/12-t/2+t2/2n Π∞m=1 (1-q nm-t)(1-qnm-(n-t)) are algebraic numbers.

AB - Let k be an imaginary quadratic field, h the complex upper half plane, and let τ ∈ h ∩ k, q = eπiτ. For n, t ∈ ℤ+ with 1 ≤ t ≤ n - 1, set n = z · 2l (z = 2, 3, 5, 7, 9, 13, 15) with l ≥ 0 integer. Then we show that q n/12-t/2+t2/2n Π∞m=1 (1-q nm-t)(1-qnm-(n-t)) are algebraic numbers.

KW - Algebraic number

KW - Rogers-Ramanujan identities

KW - Theta series

UR - https://www.scopus.com/pages/publications/50949120562

U2 - 10.4134/JKMS.2008.45.5.1379

DO - 10.4134/JKMS.2008.45.5.1379

M3 - Journal article

AN - SCOPUS:50949120562

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VL - 45

SP - 1379

EP - 1391

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 5

ER -

On the infinite products derived from theta series II

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