Martin Eichler

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

Life and work

He was born the son of the pastor Max Eichler in Pinnow in Greifswald county in Pomerania and went from 1923 to 1930 at a boarding school in Gütersloh, Westphalia. From 1930 he studied mathematics, physics and chemistry in Königsberg, Zurich ( where he to become a physicist under the influence Andreas feeder from its original target distance increased ) and from 1932 in Halle, where he in 1936 by Heinrich Brandt with the study of number theory of rational quaternion doctorate. He was first assistant in Halle, but was dismissed by the Nazi authorities as politically uncertain candidate again. Helmut Hasse gave him a job as editor of the new edition of the Encyclopedia of Mathematical Sciences, and finally caught up with him as an assistant to Göttingen, where he habilitated in 1939. During the war years he worked at the Army Research Center Peenemünde and the TU Darmstadt differential equation problems of aerodynamics. In 1947 he went to Göttingen, but spent the next two years at the Laboratory of the Royal Aircraft at Farnborough in England. In 1949 he became associate professor at the Westfälische Wilhelms-Universität in Münster, and in 1956 a full professor in Marburg. In 1959 he accepted an appointment as successor to Alexander Ostrowski to Basel.

Eichler first presented an overview of the structure and arithmetic of quaternion algebras and the theory of quadratic forms ( the generalization of his study of quaternion algebras ), about which he wrote in 1952 the book Quadratic forms and orthogonal groups. Since the 1950s, his main area was the theory of modular forms. In 1954 he proved the Ramanujan - Petersson conjecture for modular forms of weight 2 (one estimation of Fourier coefficients of modular forms, the general case later proved by Deligne ). Eichler proved for the space of modular forms of weight k = 2 one formulated by Erich Hecke guess about the basic functions of this space ("basic problem " ) and proved a trace formula for the action of Hecke operators in this space. For higher k he was a calculating way the track by recourse to integrals of modular forms ( " cohomological " methods, Eichler - Shimura theory, after Goro Shimura, the generalized this). Even in the 1980s, he wrote with Don Zagier a monograph on Jacobi forms ( modular forms with special transformation factors in module groups substitutions ).

In the 1960s, he also dealt with work on the theorem of Riemann -Roch for which he pointed out an analogy to the linear forms - Minkowski theorem in number theory in the field of body function to a variable.

Eichler was a corresponding member of the Academy of Sciences in Göttingen and honorary doctorate from the Westfälische Wilhelms -Universität Münster.

He was married since 1947 with Erika puffing ( whom he met at Peenemünde ) and had two children.