- Ludwig Stickelberger
Infobox Scientist
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birth_date =May 18 ,1850
birth_place =Buch, Schaffhausen ;
death_date =April 11 ,1936
death_place =Basel
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nationality = Swiss
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field =Mathematics
work_institutions =University of Freiburg
alma_mater =University of Heidelberg
University of Berlin
doctoral_advisor = Weierstrass
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known_for = Stickelberger relation
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footnotes =Ludwig Stickelberger (
May 18 1850 inBuch, Schaffhausen –April 11 1936 inBasel ) was aSwiss mathematician who made important contributions tolinear algebra (theory ofelementary divisors ) andalgebraic number theory (Stickelberger relation in the theory ofcyclotomic field s).Short biography
Stickelberger was born in Buch in the
canton of Schaffhausen into a family of a pastor. He graduated from a gymnasium in 1867 and studied next in theUniversity of Heidelberg . In 1874 he received a doctorate inBerlin under the direction ofKarl Weierstrass for his work on transformation ofquadratic form s to a diagonal form. In the same year he obtained hisHabilitation from Polytechnicum inZurich (nowETH Zurich ). In 1879 he became an extraordinary professor in the Albert Ludwigs University of Freiburg. From 1896 to 1919 he worked there as a full professor, and from 1919 until his return to Basel in 1924 he held the title of a distinguished professor ("ordentlicher Honorarprofessor"). He was married in 1895, but his wife and son both died in 1918. Stickelberger passed away on April 11, 1936 and was buried next to his wife and son in Freiburg.Mathematical contributions
Stickelberger's obituary lists the total of 14 publications: his thesis (in Latin), 8 further papers that he authored which appeared during his lifetime, 4 joint papers with
Georg Frobenius and a posthumously published paper written circa 1915. Despite this modest output, he is characterized there as "one of the sharpest among the pupils of Weierstrass" and a "mathematician of a high rank". Stickelberger's thesis and several later papers streamline and complete earlier investigations of various authors, in a direct and elegant way.Linear algebra
Stickelberger's work on the classification of pairs of bilinear and quadratic forms filled in important gaps in the theory earlier developed by Weierstrass and Darboux. Augmented with the contemporaneous work of Frobenius, it set the theory of
elementary divisors upon a rigorous foundation. An important 1878 paper of Stickelberger and Frobenius gave the first complete treatment of theclassification of finitely generated abelian groups and sketched the relation with the theory of modules that had just been developed by Dedekind.Number theory
Three joint papers with Frobenius deal with the theory of
elliptic function s. Today Stickelberger's name is most closely associated with his 1890 paper that established theStickelberger relation for cyclotomicGaussian sum s. This generalized earlier work of Jacobi and Kummer and was later used by Hilbert in his formulation of the reciprocity laws inalgebraic number field s. The Stickelberger relation also yields information about the structure of theclass group of acyclotomic field as a module over its abelianGalois group (cfIwasawa theory ).References
*Lothar Heffter, [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=249476 "Ludwig Stickelberger"] , Jahresbericht der Deutschen Matematische Vereinigung, XLVII (1937), pp. 79–86
* Ludwig Stickelberger, [http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=27547 "Ueber eine Verallgemeinerung der Kreistheilung"] , Mathematische Annalen 37 (1890), pp. 321–367
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