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2011•Journal of the Chungcheong Mathematical SocietyRequires access

A SIMPLE PROOF OF QUOTIENTS OF THETA SERIES AS RATIONAL FUNCTIONS OF J

Soyoung Choi

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Abstract

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that is a rational function of J, satisfying a certain condition. Where and are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

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What this paper is about

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that is a rational function of J, satisfying a certain condition. Where and are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

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Available abstract

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that is a rational function of J, satisfying a certain condition. Where and are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

Key concepts: Mathematics, Unimodular matrix, Simple (philosophy), Quotient, Series (stratigraphy), Modular form, Rational function, Invariant (physics)

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