RAMANUJAN CONTINUED FRACTIONS OF ORDER EIGHTEEN

Yoon Kyung Park

doi:10.4134/JKMS.j220180

RAMANUJAN CONTINUED FRACTIONS OF ORDER EIGHTEEN

Yoon Kyung Park

School of Natural Sciences

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

2 Scopus citations

Abstract

As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(τ). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

Original language	English
Pages (from-to)	395-406
Number of pages	12
Journal	Journal of the Korean Mathematical Society
Volume	60
Issue number	2
DOIs	https://doi.org/10.4134/JKMS.j220180
State	Published - Mar 2023

Keywords

Klein forms
modular function
Ramanujan continued fraction

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10.4134/JKMS.j220180

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title = "RAMANUJAN CONTINUED FRACTIONS OF ORDER EIGHTEEN",

abstract = "As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(τ). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.",

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N2 - As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(τ). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

AB - As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(τ). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

KW - Klein forms

KW - modular function

KW - Ramanujan continued fraction

UR - https://www.scopus.com/pages/publications/85149902874

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DO - 10.4134/JKMS.j220180

M3 - Article

AN - SCOPUS:85149902874

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VL - 60

SP - 395

EP - 406

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 2

ER -

RAMANUJAN CONTINUED FRACTIONS OF ORDER EIGHTEEN

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Keywords

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