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

Frank Patane¹

¹ Department of Mathematics Samford University 800 Lakeshore Drive Birmingham, AL 35209, U.S.A.

Acta Arithmetica, Tome 176 (2016) no. 4, pp. 343-364.

Résumé

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.

Détail

DOI : 10.4064/aa8383-6-2016

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