Martin Eichler

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Martin Eichler

Martin Maximilian Emil Eichler (born March 29, 1912 in Pinnow ; † October 7, 1992 in Arlesheim near Basel , Switzerland ) was a German mathematician who dealt with algebraic geometry and number theory.

life and work

He was born as the son of pastor Max Eichler in Pinnow in the Greifswald district in Pomerania and attended a boarding school in Gütersloh, Westphalia, from 1923 to 1930 . From 1930 he studied mathematics, physics and chemistry in Königsberg , Zurich (where, under the influence of Andreas Speiser , he refrained from his original goal of becoming a physicist) and from 1932 in Halle , where he worked with Heinrich Brandt in 1936 with investigations on the rational number theory PhD in Quaternion Algebras. He was initially an assistant in Halle, but was dismissed by the National Socialist authorities as a politically insecure candidate. Helmut Hasse got him a job as editor of the new edition of the Encyclopedia of Mathematical Sciences and finally brought him to Göttingen as an assistant , where he completed his habilitation in 1939. During the war years he worked at the Peenemünde Army Research Institute and at the Technical University of Darmstadt on differential equation problems from aerodynamics . In 1947 he went back to Göttingen, but spent the next two years at the Royal Aircraft Research Institute in Farnborough in England. In 1949 he became associate professor at the Westphalian Wilhelms University in Münster and in 1956 full professor in Marburg . In 1959 he followed a call to Basel to succeed Alexander Ostrowski .

Eichler first dealt with the structure and arithmetic of quaternion algebras and with the theory of quadratic forms (the generalization of his study on quaternion algebras), about which he wrote the book Quadratic forms and orthogonal groups in 1952 . From the 1950s onwards, his main area of ​​work was the theory of modular forms . In 1954 he proved the Ramanujan-Petersson conjecture for modular forms of weight 2 (an estimate of the Fourier coefficients of the modular forms, the general case later proved by Pierre Deligne ). For the space of modular forms with weight k = 2, Eichler proved a conjecture formulated by Erich Hecke about the basic functions of this space (“basic problem”) and proved a trace formula for the effect of Hecke operators in this space. For higher k he gave a possibility to calculate the track by using integrals of modular forms ("cohomological" methods, Eichler-Shimura theory, according to Gorō Shimura , who generalized this). In the 1980s he and Don Zagier wrote a monograph on Jacobiforms .

In the 1960s he also worked on the Riemann-Roch theorem , for which he showed an analogy to Minkowski's linear form theorem in number theory in the field of the function fields of a variable .

From 1978 Eichler was a corresponding member of the Academy of Sciences in Göttingen and an honorary doctorate from the Westphalian Wilhelms University of Münster .

He was married to Erika Paffen (whom he met in Peenemünde ) since 1947 and had two sons, one of whom is the physicist Ralph Eichler .

literature

  • Martin Kneser Martin Eichler (1912-1992) , Acta Arithmetica , Volume 65, 1993, pp. 293-296.
  • Jürg Kramer Life and Work of Martin Eichler , Elements of Mathematics, Volume 49, 1994, pp. 45–60. Revised version, pdf

Fonts (selection)

Web links

Individual evidence

  1. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 74.
personal data
SURNAME Eichler, Martin
ALTERNATIVE NAMES Eichler, Martin Maximilian Emil
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH March 29, 1912
PLACE OF BIRTH Pinnow , Greifswald district
DATE OF DEATH October 7, 1992
Place of death Basel