Kurt Heegner

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Kurt Heegner (born December 16, 1893 in Berlin , † February 2, 1965 in West Berlin ( Berlin-Steglitz )) was a German mathematician, physicist and engineer. He lived and worked in Berlin and became known for his number theoretic discoveries.

Life

Heegner's father Otto, who died in 1910, was a clerk accountant ( chief calculator ) in the service of the German Reich and most recently an accountant . His marriage to Clara Fechner had three sons and a daughter.

Heegner graduated from the Askanisches Gymnasium in Berlin in 1913 and studied mathematics and physics in Berlin with Hermann Amandus Schwarz , Konrad Knopp , Max Planck , Arthur Wehnelt and Heinrich Rubens until 1917 . During the First World War he had been drafted into the military since 1917 and was involved in radio research, probably in Berlin. It was there that he became interested in electronics. In 1920 he did his doctorate in Jena under Walter Rogowski , his former superior in military research during the First World War, with a thesis on intermediate circuit tube transmitters in which elliptical curves are also discussed. In the 1920s and 1930s (most recently in 1938) he published various articles on the generation of vibrations with electron tube circuits and piezo crystals , among others with the Japanese Watanabe. He also registered patents, such as one on the Heegner circuit (1933), which he initially licensed to the Loewe company ; but at the end of the 1930s there were negotiations with Telefunken , who also wanted to use it for army deliveries. Until the end of the war he received considerable license fees from it. From 1932 to 1946 he was a private scholar in Berlin, where he completed his habilitation in mathematics (Dr. habil.) In 1939 with the work Transformable automorphic functions and quadratic forms and his other work published in the Mathematische Zeitschrift . Werner Weber and Erhard Schmidt held the oral exam . A first mathematical publication followed in 1929/30 and 1932 after several revisions, after the speaker Erich Hecke found the representation incomprehensible and out of date and Hasse asked the Bonn mathematician Erich Bessel-Hagen during his stay in Berlin, Heegner to revise it in the language of the modern Algebra to help. From the 1930s to 1956 he published several works a. a. on elliptic and automorphic functions , Abelian integrals and quadratic forms e.g. B. in the Mathematische Annalen and the Mathematische Zeitschrift.

Around 1946, apparently by chance, he came into contact again with Erhard Schmidt, who after the war rebuilt mathematics at Berlin University and lived near Heegner. He mentioned his work on the Gauss problem in passing, and Schmidt and Helmut Hasse (who had already been in contact with Heegner in the 1930s on the occasion of the publication of various papers in the Crelle's Journal) found him a job at the Zentralblatt für Mathematik at the Research Institute for Mathematics of the Academy of Sciences where he was from 1947 to 1950. Then he lived in seclusion in Berlin-Steglitz. He never seems to have tried to get a permanent job at a university and his habilitation only served to gain recognition as a mathematician.

He died impoverished in his apartment in Berlin-Steglitz, where he had lived since 1932 (Elisenstrasse 7). He was found on February 2nd, but probably died several days earlier around January 31st. Most recently, he was supported by his sister Lotte Hensel, who was married to the mathematics teacher Ernst Hensel (not related to Kurt Hensel ). Heegner was single and lived with his mother for a long time, who was also a financial source of support with her widow position. She died in 1942. He was considered cranky and devoted himself intensively to religious studies. For example, the manuscript of his work on the Gaussian class number problem is titled with the recitative of Cantata No. 51 by Johann Sebastian Bach . Neighbors later knew him as Jesus von Steglitz . He had a long white beard and a ponytail hairstyle. During the Second World War, he showed courage by staying in his apartment during the bombing and removing incendiary devices that had been dropped in the house. He also stood by his older brother Fritz, who had a Jewish wife.

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At Schwarz's suggestion, he dealt with Ernst Eduard Kummer's problem of defining all squares with rational sides and diagonals and tetrahedra with rational sides and volumes. Heegner used the theory of elliptic functions and module functions.

In 1952 Heegner published a proof of a conjecture already made by Carl Friedrich Gauß about the number of imaginary-quadratic number fields with class number 1 in number theory ( Gauss's class number problem ). Heegner had previously published several papers on module functions . Because the evidence was difficult to understand, contained some minor errors, and came from an academic outsider, it was not recognized for years. It was not until Harold Stark found similar evidence in 1967 that was equivalent to Heegner's evidence that Heegner was also recognized after his death. Besides Stark, Max Deuring , Curt Meyer and Carl Ludwig Siegel also played a role .

The Heegner numbers , which play a role in the problem mentioned, as well as Heegner points (from Bryan Birch ) in the number theory of elliptic curves are named after Heegner . Heegner was the first to combine the problem of congruent numbers with elliptic curves, and in 1952 he proved that a prime number is a congruent number if or . Most of the later results in this direction (e.g. Jerrold Tunnell's methods ) presuppose the unproven Birch and Swinnerton-Dyner conjecture.

His estate, which also includes unpublished mathematical works, came to Max Deuring through his sister Lotte and is now in the Göttingen State and University Library . Documents on his patents can be found in the Telefunken Archive in the German Museum of Technology in Berlin.

Fonts

literature

Web links

Individual evidence

  1. ↑ The corresponding publication appeared in the Archiv für Elektrotechnik, Volume 9, 1920
  2. ↑ In this context, personal information about Heegner can also be found in the Telefunken archive. In a protocol from Telefunken on negotiations with Heegner in Berlin on March 31, 1939, it says literally: He speaks unclearly and incomprehensibly as always (according to his negotiating partner Dr. Bechmann). In a 1941 report by a private detective for Telefunken, he is described as a private scholar who lives with his mother and does not work on anyone's behalf. He is described as undemanding and living in orderly circumstances.
  3. ↑ 3 parts, Mathematische Zeitschrift, Volume 43, 1937, pp. 161-204, 321-352, Volume 44, 1938, 555-567
  4. ↑ Diophantine investigations into reducible abelian integrals, 2 parts, Mathematische Zeitschrift, Volume 31, 1929/30, pp. 457-480, 481-497
  5. ↑ About an algebraic task that occurs in the reduction and transformation theory of algebraic functions , Crelles Journal (Journal for Pure and Applied Mathematics), Volume 168, 1932, Originally it was called About the transformation of elliptic functions
  6. ↑ Patterson, Oberwolfach Report 2008, see literature. Then he warmed himself up in Schmidt's apartment because his own was unheated.
  7. ^ Patterson, Oberwolfach Report 2008, p. 1356
  8. ↑ Schappacher, lecture on Heegner, Paris 2009, see web links
  9. ↑ Stark: On the “gap” in a theorem of Heegner , Journal of Number Theory, Volume 1, 1969, pp. 16–27, Max Deuring: Imaginary quadratic number fields with the class number one ( Memento of the original from November 30, 2015 in Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Inventiones Mathematicae Volume 5, 1968, p. 169, Carl Ludwig Siegel: To the proofs of Stark's theorem , Inventiones Mathematicae Volume 5, 1968, p. 180 @1@ 2Template: Webachiv / IABot / gdz.sub.uni-goettingen.de
personal data
SURNAME Heegner, Kurt
BRIEF DESCRIPTION German engineer, physicist and mathematician
DATE OF BIRTH December 16, 1893
PLACE OF BIRTH Berlin
DATE OF DEATH February 2, 1965
Place of death Berlin