Martin Eichler

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

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.

Selected publications Quadratische Formen und orthogonale Gruppen, Springer 1952, 1974

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); with Don Zagier: The Theory of Jacobi forms, Birkhäuser 1985;

Allgemeine Integration linearer partieller Differentialgleichungen von elliptischem Typ bei zwei Grundvariablen, Abh. Math. Sem. Univ. Hamburg 15 (1947), 179–210. On the differential equation uxx + uyy + N(x)u = 0, Trans. Amer. Math. Soc. 65 (1949), 259–278

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)

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 , Mathem. Annalen 1967, (Eichler–Shimura theory) 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