Hans Arnold Heilbronn

Hans Arnold Heilbronn (born October 8, 1908 in Berlin , † April 28, 1975 in Toronto ) was a German-born British-Canadian number theorist .

life and work

Heilbronn studied at the Friedrich-Wilhelms-Universität zu Berlin and became a member of the Ghibellinia Landsmannschaft in the Burschenbunds-Convent . He moved to the Albert Ludwig University of Freiburg and the Georg August University of Göttingen . He received his doctorate in 1931 with a doctoral thesis under Edmund Landau with the improvement of a theorem by Guido Hoheisel about gaps between prime numbers. As a Jew, Heilbronn fled Germany to England in 1933, where he found a job at the University of Bristol after stops in Cambridge and Manchester .

In Germany, after his emigration, Heilbronn was targeted by the National Socialist police, who classified him as an important target: In the spring of 1940, the Reich Security Main Office in Berlin placed him on the special wanted list GB , a directory of people who would be killed in the event of a successful invasion and occupation of the British Isles by the Wehrmacht, special SS commandos following the occupation forces were to be identified and arrested with special priority.

Here he used methods of analytical number theory to prove that the class number of imaginary quadratic number fields with d approaches infinity. He also proved, together with Edward Linfoot, that there are at most 10 such number fields with the class number 1 (nine had been known since Gauss), an important advance in the problem of determining all such number fields for a given class number from Carl Friedrich Gauß . After this work he received an invitation from Louis Mordell to Manchester and a year later (under the influence of Godfrey Harold Hardy ) a scholarship to Trinity College at Cambridge University , where he worked on improvements with Harold Davenport , whom he still knew from Göttingen the Hardy-Littlewood circle method worked. He also worked on the Waring problem , number field with Euclidean algorithm and proved that the Riemann Hypothesis does not hold for Epstein's zeta function . He was interned briefly in World War II and then in the British Army with the military secret service. In 1946 he went back to Bristol, where he became professor and dean of the faculty in 1949. In 1964 he moved to the United States, initially at the invitation of Olga Taussky-Todd to the California Institute of Technology . 1964 to 1975 he was a professor at the University of Toronto . In 1970 he became a Canadian citizen. He died during a pacemaker operation. ${\displaystyle \mathbb {Q} ({\sqrt {-d}})}$

Heilbronn became a Fellow of the Royal Society in London in 1951 . From 1959 to 1961 he was President of the London Mathematical Society .

His students include the Indian Sarvadaman Chowla and Albrecht Fröhlich .

Fonts

• Collected Papers , Wiley 1988
• On the class number of imaginary quadratic fields , Quarterly Journal of Mathematics Vol. 5, 1934, pp. 150-160
• with Linfoot: On the imaginary quadratic corpora of class number one , Quarterly Journal of Mathematics, Vol. 5, 1934, pp. 293-301

literature

• Linfoot: A brief collaboration: Heilbronn and Linfoot 1933-35 , Math.Intelligencer 1993, No. 3
• Cassels, Fröhlich: Biographical Memoirs of the Fellows of the Royal Society 1976, and Bulletin London Mathematical Society 1977

Web links

• John J. O'Connor, Edmund F. Robertson :  Hans Arnold Heilbronn. In: MacTutor History of Mathematics archive .

Remarks

1. ^ Kurt Naumann: Directory of the members of the old gentlemen's association of BC Munich e. V. and all other former BCers as well as the old men of the Wiener SC . Saarbrücken, Christmas 1962, p. 23.
2. ↑ Hoheisel had proved that there is a there, so for sufficiently large x always a prime between x and is ${\displaystyle u<1}$ ${\displaystyle x^{u}}$
3. ^ Entry for Heilbronn on the special wanted list GB (reproduction on the website of the Imperial War Museum in London)