Siegelsche Modulfunktionen by Eberhard Freitag (auth.)

By Eberhard Freitag (auth.)

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Daß im Falln22 kein Regularitätsverhalten in den Spitzen zu fordern ist, wurde von M. Koecher entdeckt. 15 (s. 15 weiter unten) wurden erstmals von M. Eichler mit einer etwas anderen Methode bewiesen [20]. Er benutzte die Fourier-JacobiEntwicklung einer Modulform (s. A IV). § 4. Poincare-Reihen Nach den Thetareihen lernen wir nun ein zweites wichtiges Konstruktionsverfahren für Modulformen kennen. Poincarereihen erhält man durch Mittelung von Funktionen f: ll-I n .....

E, Z* =M

6 Hilfssatz. Wenn das letzte Diagonalelement tnn einer semipositiven Matrix T verschwindet, so T= gilt (~l ~), Tl = Ti n - l )~O. Beweis. Man nutze aus, daß jede zweireihige Unterdeterminante von T nicht negativ ist. 7 Bemerkung. Der

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