Autorentext

Biography of Helmut Hasse (1898-1979) Born on August 25, 1898 in Kassel, Germany, Helmut Hasse studied at the University of Göttingen after WWI. Of his teachers there including Landau, Hilbert and Ehmy Noether, Hecke influenced him most. In 1820, Hasse went to Marburg, and under the direction of Kurt Hensel, discovered what is now known as the Hasse principle, or "local-global" principle, in algebraic number theory. He held further positions at the universities in Kiel and Hall prior to 1933. With the troubles of 1933, Hermann Weyl, who had succeeded Hilbert in the foremost chair or mathematics in Germany, resigned and Helmut Hasse was appointed in this place. The following year, Hasse became director of the Mathematical Institute at Göttingen. From 1939 to 1945, Hasse worked in Berlin for the navy on problems in ballistics. He returned to Göttingen but was soon dismissed by the British occupation forces. In 1946 he took a research position at the Berlin Academy. Thereafter, he held positions at the Humboldt University in East Berlin, and, from 1950 until retirement in 1966, at the University of Hamburg. At Halle, Hasse obtained fundamental results on the structure of central simple algebras over local fields. In Marburg, he did joint work with Brauer and Emmy Noether on simple algebras, also on elliptic curves and topological fields. In particular, he proved the analogon of the Riemann Hypothesis for zeta functions of elliptic curves. Both of Hasse s famous books Über die Klassenzahl abelscher Zahlkörper und Zahlentheorie appeared during his years in Berlin.

Inhalt
Erster Abschnitt Grundlagen.- § 1. Primzerlegung.- § 2. Größter gemeinsamer Teiler.- § 3. Vollkommene Zahlen, Mersennesche und Fermatsche Primzahlen.- § 4. Kongruenz, Restklassen.- § 5. Die Struktur der primen Restklassengruppen.- Zweiter Abschnitt Quadratische Reste.- § 6. Definition, Reduktion, Kriterien.- § 7. Das quadratische Reziprozitätsgesetz: Elementarer Beweis.- § 8. Das quadratische Reziprozitätsgesetz: Beweis mit Gaußschen Summen.- § 9. Die Jacobische Verallgemeinerung.- § 10. Verteilungsfragen über quadratische Reste nach einer Primzahl.- Dritter Abschnitt Der Dirichletsche Primzahlsatz.- § 11. Elementare Sonderfälle.- § 12. Die Methode von Dirichlet.- §13. Die Charaktere endlicher abelscher Gruppen, Restklassencharaktere.- § 14. Der Beweis von Dirichlet.- § 15. Das Nichtverschwinden der L-Reihen.- Vierter Abschnitt Quadratische Zahlkörper.- § 16. Elementare Teilbarkeitslehre.- § 17. Divisorentheorie.- § 18. Bestimmung der Klassenzahl.- § 19. Quadratische Zahlkörper und quadratisches Reziprozitätsgesetz.- § 20. Systematische Theorie der Gaußschen Summen.- Namenverzeichnis.