Martin Eichler

Martin Maximilian Emil Eichler 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, 1974Einführung in die Theorie der algebraischen Zahlen und Funktionen, Birkhäuser 1963; Eng. trans. 1966,, in which a section on modular forms is added; pbk 2014 reprint of 1963 German originalProjective varieties and modular forms 1971 ;

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, 179–210. On the differential equation u_xx + u_yy + Nu = 0, Trans. Amer. Math. Soc. 65, 259–278
, with errata
Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenz-Zetafunktion, Archiv Math. vol. 5, 1954, pp. 355–366 Quadratische Formen und Modulfunktionen Acta Arithmetica vol. 4, 1958, pp. 217–239
, Mathem. Annalen 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