Martin Eichler

Martin Maximilian Emil Eichler (29 March 1912 – 7 October 1992) was a German number theorist.

Martin Eichler
Martin Eichler
Born(1912-03-29)29 March 1912
Died7 October 1992(1992-10-07) (aged 80)
NationalityGerman
Scientific career
FieldsNumber theory and Mathematics

Eichler received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.

Eichler and Goro Shimura developed a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.[1][2]

Selected publications
  • Quadratische Formen und orthogonale Gruppen, Springer 1952,[3] 1974
  • Lectures on Modular Correspondences. Tata Institute. 1955; pbk, 169 pages
  • Einführung in die Theorie der algebraischen Zahlen und Funktionen, Birkhäuser 1963; Eng. trans. 1966, Introduction to the theory of algebraic numbers and functions, in which a section on modular forms is added; pbk 2014 reprint of 1963 German original
  • Projective varieties and modular forms 1971 (Riemann-Roch theorem); 2006 edition.
  • with Don Zagier: The Theory of Jacobi forms, Birkhäuser 1985; 2013 edition.
  • Über die Einheiten der Divisionsalgebren, Mathem. Annalen 1937
  • Neuere Ergebnisse der Theorie der einfachen Algebren, Jahresbericht DMV 1937
  • Allgemeine Integration linearer partieller Differentialgleichungen von elliptischem Typ bei zwei Grundvariablen, Abh. Math. Sem. Univ. Hamburg 15 (1947), 179–210. MR0029054
  • On the differential equation uxx + uyy + N(x)u = 0, Trans. Amer. Math. Soc. 65 (1949), 259–278 doi:10.1090/S0002-9947-1949-0029055-8
  • Zur Algebra der orthogonalen Gruppen Mathem. Zeitschrift 1950
  • Zahlentheorie der Quaternionenalgebren, Crelle J. vol. 195, 1955, with errata
  • Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenz-Zetafunktion, Archiv Math. vol. 5, 1954, pp. 355–366 (Ramanujan-Petersson conjecture)
  • Eine Verallgemeinerung der Abelschen Integrale, Math. Zeitschrift vol. 67, 1957, pp. 267-298
  • Quadratische Formen und Modulfunktionen Acta Arithmetica vol. 4, 1958, pp. 217–239
  • Eine Vorbereitung auf den Riemann-Rochschen Satz für algebraische Funktionenkörper, Crelle J. 1964
  • Einige Anwendungen der Spurformel im Bereich der Modularkorrespondenzen, Mathem. Annalen 1967, (Eichler-Shimura theory)
  • Eichler Eine Spurformel von Korrespondenzen von algebraischen Funktionenkörpern mit sich selber, Inv. Math. vol. 2, 1967 with corrections
  • The basis problem for modular forms and the traces of the Hecke operators, Springer, Lecture notes Math. vol.320, 1973, pp. 75–152
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See also

References
  1. Richard Taylor (2012). "Modular Arithmetic: Driven by Inherent Beauty and Human Curiosity". Institute for Advanced Study. Retrieved 2014-12-22.
  2. Edward Frenkel. Love and Math: The Heart of Hidden Reality. pp. 90. ISBN 978-0465050741.
  3. Whaples, G. (1955). "Review: Quadratische Formen und orthogonale Gruppen by Martin Eichler". Bull. Amer. Math. Soc. 61: 589–593. doi:10.1090/S0002-9904-1955-10001-8.


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