Oberseminar WiSe 2010/11 Zusammenfassung des Vortrags von Georg Hein (Essen)
From quadratic forms to modular forms
The theta series of an integral quadratic form is a modular form. Unfortunately this invariant is not fine enough to distinguish equivalence classes of quadratic forms. I will sketch a construction of pairs of inequivalent quadratic forms which are isospectral, which means they have the same theta series. Finally I will introduce a generalization of the theta series which allows the distinction of the above pairs.