Helmut Hasse

Helmut Hasse
Born	(1898-08-25)25 August 1898 Kassel, Hesse-Nassau, Prussia
Died	26 December 1979(1979-12-26) (aged 81) Ahrensburg, Schleswig-Holstein, West Germany
Nationality	German
Fields	Mathematics
Alma mater	University of Marburg University of Göttingen
Doctoral advisor	Kurt Hensel
Doctoral students	Cahit Arf Wolfgang Franz Paul Lorenzen Curt Meyer Günter Pickert Hans Reichardt Peter Roquette Otto Schilling Oswald Teichmüller
Other notable students	Paul Lorenzen

Helmut Hasse (German: ; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry (Hasse principle), and to local zeta functions.

Life

He was born in Kassel, and died in Ahrensburg.

After serving in the navy in World War I, he studied at the University of Göttingen, and then at Marburg under Kurt Hensel, writing a dissertation in 1921 containing the Hasse–Minkowski theorem, as it is now called, on quadratic forms over number fields. He then held positions at Kiel, Halle and Marburg. He was Hermann Weyl's replacement at Göttingen in 1934. Politically, he was a right-wing nationalist and applied for membership in the Nazi Party in 1937, but this was denied to him due to his Jewish ancestry. After the war, he briefly returned to Göttingen in 1945, but was excluded by the British authorities. After brief appointments in Berlin, from 1948 on he settled permanently as professor in Hamburg.

He collaborated with many mathematicians, in particular with Emmy Noether and Richard Brauer on simple algebra, and with Harold Davenport on Gauss sums (Hasse–Davenport relations), and with Cahit Arf on the Hasse–Arf theorem.

Publications

• Mathematische Abhandlungen, H.W.Leopoldt, Peter Roquette (ed.), 3 vols., de Gruyter 1975
• Number theory, Springer, 1980, 2002 (Eng. trans. of Zahlentheorie, 3rd edn., Akademie Verlag 1969)^[1]
• Vorlesungen über Zahlentheorie, Springer, 1950^[1]
• Über die Klassenzahl abelscher Zahlkörper, Akademie Verlag, Berlin, 1952.^[2]
• Höhere Algebra vols. 1, 2, Sammlung Göschen, 1967, 1969
• Vorlesungen über Klassenkörpertheorie, physica Verlag, Würzburg 1967
• Hasse, H. (1926), "Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. I: Klassenkörpertheorie.",  
• Hasse, H. (1927), "Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Teil Ia: Beweise zu I.",  
• Hasse, H. (1930), "Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper. Teil II: Reziprozitätsgesetz",  
• Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, 1965 (reprint from Berichts aus dem Jahresbericht der DMV 1926/27)
• New edn. of Algebraische Theorie der Körper by Ernst Steinitz, together with Reinhold Baer, with a new appendix on Galois theory. Walter de Gruyter 1930.
• Hasse Mathematik als Wissenschaft, Kunst und Macht, DMV Mitteilungen 1997, Nr.4 (Published version of a lecture given at the University of Hamburg 1959)
• Hasse „Geschichte der Klassenkörpertheorie“, Jahresbericht DMV 1966
• Hasse „Die moderne algebraische Methode“, Jahresbericht DMV 1930
• Brauer, Hasse, Noether „Beweis eines Hauptsatzes in der Theorie der Algebren“, Journal reine angew.Math. 1932
• Hasse „Theorie der abstrakten elliptischen Funktionenkörper 3- Riemann Vermutung“, Journal reine angew. Math., 1936
• Hasse „Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen“, Journal reine angew.Math. 1923

See also

• Hasse diagram
• Hasse invariant of an elliptic curve
• Hasse invariant of a quadratic form
• Artin–Hasse exponential
• Hasse–Weil L-function
• Hasse norm theorem
• Hasse's algorithm
• Hasse's theorem on elliptic curves

References

External links

• .  
• Another biography
• Helmut Hasse at the Mathematics Genealogy Project