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

For two even unimodular positive de¯nite integral qua- dratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1]showed that µA(¿ )=µB(¿ ) is a rational function of J, satisfying a certain condition. Where µA(¿ ) and µB(¿ ) are theta series related to A[X] and B[X], respectively, and J is the classical modular in-variant. In this paper we give a simple proof of Theorem 1 of [1].

1. Introduction

2. A simple proof of Theorem 1.1

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