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1999•Journal of the Korean Mathematical SocietyRequires access

ARITHMETIC OF THE MODULAR FUNCTION $j_4$

Chang-Heon Kim, Ja-Kyung Koo

Open publisher page 4 citations

Abstract

Since the modular curve has genus 0, we have a field isomorphism K(X(4)){\approx}\mathcal{C}(j_{4})$ where is a quotient of Jacobi theta series ([9]). We derive recursion formulas for the Fourier coefficients of and (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.

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What this paper is about

Since the modular curve has genus 0, we have a field isomorphism K(X(4)){\approx}\mathcal{C}(j_{4})$ where is a quotient of Jacobi theta series ([9]). We derive recursion formulas for the Fourier coefficients of and (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Since the modular curve has genus 0, we have a field isomorphism K(X(4)){\approx}\mathcal{C}(j_{4})$ where is a quotient of Jacobi theta series ([9]). We derive recursion formulas for the Fourier coefficients of and (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.

Key concepts: Mathematics, Modular form, Fourier series, Isomorphism (crystallography), Quotient, Modular design, Series (stratigraphy), Function field

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