An identity connecting theta series associated with binary quadratic forms of discriminant Delta and Delta p^2

When/Where:

October 7, 2014, at 1:55pm, in LIT 368

Abstract:

I will state and prove a new identity which connects theta series associated with binary quadratic forms of idoneal discriminants \( \Delta\) and \(\Delta p^2\), for \(p\) a prime. I will then illustrate how to use this identity to derive Lambert series identities and hence product representation formulas for certain forms. Last but not least, I discuss generalizations to non-idoneal discriminants and the resulting theta series identities one may derive.