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, 1974
  • Einführung 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 original
  • Projective 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 uxx + uyy + 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