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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.