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Martin Eichler

{{Short description|German mathematician (1912–1992)}}

{{Infobox scientist

| name = Martin Eichler

| image = Martin Eichler.jpg

| caption = Martin Eichler

| birth_date = {{Birth date|1912|3|29|df=y}}

| birth_place =

| death_date = {{death date and age|1992|10|7|1912|3|29|df=y}}

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| residence =

| nationality = German

| field = Number theory and Mathematics

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}}

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

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.{{cite web | url=https://www.ias.edu/about/publications/ias-letter/articles/2012-summer/modular-arithmetic-taylor | title=Modular Arithmetic: Driven by Inherent Beauty and Human Curiosity | work=Institute for Advanced Study

| author=Richard Taylor

| date=2012

| access-date=2014-12-22 }}

{{cite book|isbn=978-0465050741|title=Love and Math: The Heart of Hidden Reality|url=https://archive.org/details/lovemathheartofh0000fren|url-access=registration|author=Edward Frenkel|author-link=Edward Frenkel|pages=[https://archive.org/details/lovemathheartofh0000fren/page/90 90]}}

Selected publications

  • Quadratische Formen und orthogonale Gruppen, Springer 1952,{{cite journal|title=Review: Quadratische Formen und orthogonale Gruppen by Martin Eichler|author=Whaples, G.|journal=Bull. Amer. Math. Soc.|volume=61|year=1955|pages=589–593|doi=10.1090/S0002-9904-1955-10001-8|doi-access=free}} 1974
  • {{cite book|title=Lectures on Modular Correspondences|publisher=Tata Institute|year=1955|postscript=; pbk, 169 pages}}
  • Einführung in die Theorie der algebraischen Zahlen und Funktionen, Birkhäuser 1963; Eng. trans. 1966, [https://books.google.com/books/about/Introduction_to_the_Theory_of_Algebraic.html?id=E09i81munMAC 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); {{cite book|title=2006 edition|isbn = 9783540368694|url=https://books.google.com/books?id=P9LnCAAAQBAJ|last1 = Eichler|first1 = M.|date = 15 November 2006| publisher=Springer }}
  • with Don Zagier: The Theory of Jacobi forms, Birkhäuser 1985; {{cite book|title=2013 edition|isbn = 9781468491623|url=https://books.google.com/books?id=p_PTBwAAQBAJ|last1 = Eichler|first1 = Martin|last2 = Zagier|first2 = Don|date = 14 December 2013| publisher=Springer }}
  • [https://archive.today/20130106070430/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=38040 Über die Einheiten der Divisionsalgebren, Mathem. Annalen 1937]
  • [https://archive.today/20130212080408/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=249488 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. {{MR|0029054}}
  • 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}}
  • [https://archive.today/20130212061450/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=18238 Zur Algebra der orthogonalen Gruppen Mathem. Zeitschrift 1950]
  • [https://web.archive.org/web/20151216205623/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=260643 Zahlentheorie der Quaternionenalgebren, Crelle J. vol. 195, 1955], with errata [https://web.archive.org/web/20151222003559/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=260614]
  • Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenz-Zetafunktion, Archiv Math. vol. 5, 1954, pp. 355–366 (Ramanujan–Petersson conjecture)
  • [https://archive.today/20130212094933/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=159683 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
  • [https://web.archive.org/web/20160107132925/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=261591 Eine Vorbereitung auf den Riemann-Rochschen Satz für algebraische Funktionenkörper, Crelle J. 1964]
  • [https://archive.today/20130106080009/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=68043 Einige Anwendungen der Spurformel im Bereich der Modularkorrespondenzen], Mathem. Annalen 1967, (Eichler–Shimura theory)
  • [https://archive.today/20130212114312/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=166692 Eichler Eine Spurformel von Korrespondenzen von algebraischen Funktionenkörpern mit sich selber, Inv. Math. vol. 2, 1967] with corrections [https://archive.today/20130212122357/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=166721]
  • 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

References

{{Reflist}}

External links

  • {{MacTutor Biography|id= Eichler}}
  • Martin Kneser, [https://web.archive.org/web/20040807155848/http://www.numbertheory.org/obituaries/AA/eichler/ Martin Eichler (1912-1992)], Acta Arithmetica vol. 65, 1993, pp. 293–296, Obituary (in German).
  • Jürg Kramer, [http://didaktik.mathematik.hu-berlin.de/files/eichler-neu.pdf Leben und Werk von Martin Eichler], Elemente der Mathematik vol. 49, 1994, pp. 45–60.

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{{DEFAULTSORT:Eichler, Martin}}

Category:1912 births

Category:1992 deaths

Category:20th-century German mathematicians

Category:German number theorists

Category:Academic staff of the University of Münster

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