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Abstract

When the discriminants $\varDelta $ and $\varDelta p^2$ have one form per genus, Patane (2015) proves a theorem which connects the theta series associated to binary quadratic forms of each discriminant. This paper generalizes the main theorem of Patane (2015) by allowing $\varDelta $ and $\varDelta p^2$ to have multiple forms per genus. In particular, we state and prove an identity which connects the theta series associated to a single binary quadratic form of discriminant $\varDelta $ to a theta series associated to a subset of binary quadratic forms of discriminant $\varDelta p^2$. Here and everywhere $p$ is a prime.