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].
Keywords
modular forms; modular J-invariant;
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1
J. K. Koo, Quotients of theta series as rational functions of J and , Math. Z. 202 (1989), no. 3, 367-373.
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