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
Died	7 October 1992(1992-10-07) (aged 80)
Nationality	German
Scientific career
Fields	Number 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{{cite book}}: CS1 maint: postscript (link)
• 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); Eichler, M. (15 November 2006). 2006 edition. ISBN 9783540368694.
• with Don Zagier: The Theory of Jacobi forms, Birkhäuser 1985; Eichler, Martin; Zagier, Don (14 December 2013). 2013 edition. ISBN 9781468491623.
• Über die Einheiten der Divisionsalgebren, Mathem. Annalen 1937^{[permanent dead link]}
• Neuere Ergebnisse der Theorie der einfachen Algebren, Jahresbericht DMV 1937^{[permanent dead link]}
• 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 u_xx + u_yy + 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^{[permanent dead link]}
• , 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^{[permanent dead link]}
• Quadratische Formen und Modulfunktionen Acta Arithmetica vol. 4, 1958, pp. 217–239
• Einige Anwendungen der Spurformel im Bereich der Modularkorrespondenzen^{[permanent dead link]}, Mathem. Annalen 1967, (Eichler–Shimura theory)
• Eichler Eine Spurformel von Korrespondenzen von algebraischen Funktionenkörpern mit sich selber, Inv. Math. vol. 2, 1967^{[permanent dead link]} with corrections [2]^{[permanent dead link]}
• The basis problem for modular forms and the traces of the Hecke operators, Springer, Lecture notes Math. vol.320, 1973, pp. 75–152

See also

• Eichler–Shimura congruence relation
• Eichler–Shimura isomorphism
• Eichler cohomology
• Eichler order
• Eichler's proof of the CBH theorem

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.

External links

• O'Connor, John J.; Robertson, Edmund F., "Martin Eichler", MacTutor History of Mathematics archive, University of St Andrews
• Martin Kneser, , Acta Arithmetica vol. 65, 1993, pp. 293–296, Obituary (in German).
• Jürg Kramer, Leben und Werk von Martin Eichler, Elemente der Mathematik vol. 49, 1994, pp. 45–60.