کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4593513 | 1630658 | 2015 | 27 صفحه PDF | دانلود رایگان |
We state and prove an identity which connects theta series associated with binary quadratic forms of idoneal discriminants Δ and Δp2Δp2, for p a prime. Employing this identity, we extend the results of Toh [8] by writing the theta series of forms of discriminant Δp2Δp2 as a linear combination of Lambert series. We then use these Lambert series decompositions to give explicit representation formulas for the forms of discriminant Δp2Δp2. Lastly, we give a generalization of our main identity, which employs a map of Buell [4] to connect forms of discriminant Δ to Δp2Δp2. Our generalized identity links theta series associated with a single form of discriminant Δ to a theta series associated with forms of discriminant Δp2Δp2, where Δ and Δp2Δp2 are no longer required to be idoneal.
Journal: Journal of Number Theory - Volume 156, November 2015, Pages 290–316