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On a generalized identity connecting theta series associated with discriminants $\varDelta $ and $\varDelta p^2$

Volume 176 / 2016

Frank Patane Acta Arithmetica 176 (2016), 343-364 MSC: 11E16, 11E25, 11F27, 11H55, 11R29. DOI: 10.4064/aa8383-6-2016 Published online: 28 October 2016


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.


  • Frank PataneDepartment of Mathematics
    Samford University
    800 Lakeshore Drive
    Birmingham, AL 35209, U.S.A.

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