Ludwig Stickelberger

Ludwig Stickelberger (born May 18, 1850 in Buch ; † April 11, 1936 in Basel ) was a Swiss mathematician .

Stickelberger was born as a pastor's son in Buch in the canton of Schaffhausen . In 1867 he graduated from the humanistic grammar school in Schaffhausen and studied in Heidelberg and Berlin . From 1872 to 1874 he worked as a high school teacher in Schaffhausen and Schiers . In 1874 he was at Karl Weierstrass in Berlin with a thesis on the transformation of quadratic forms in diagonal form (De problemate quodam ad duarum bilinearium vel quadraticarum transformationem pertinent) PhD . In the same year he completed his habilitation at the Polytechnic in Zurich , where he worked as a private lecturer until 1879. In 1879 he became associate professor in Freiburg im Breisgau . From 1894 to 1919 he was a full professor there and then until 1924 a full honorary professor. In 1925 he moved to Basel, Switzerland . In 1895 he became a member of the Leopoldina . From 1909 to 1924 he was an associate member of the Heidelberg Academy of Sciences and Humanities.

His investigations concern different areas of algebra (for example with his friend Ferdinand Georg Frobenius on group theory), analysis and number theory, in which he showed himself to be "one of the most astute students of Weierstrass" (Heffter in his obituary). Above all, his work on the field of circular division (on the generalization of circular division) is known. There, Stickelberger's theorem explicitly provides formal sums of elements of the Galois group of the circle division , which, when applied to any ideal in the ring of whole numbers of the circle, result in a main ideal. " Annihilates " the ideal , it is an annihilitor of the ideal class group of . According to Stickelberger's theorem, is a multiple of the Stickelberger element ${\displaystyle S}$ ${\displaystyle G=\{\sigma _{a}|a\in (\mathbb {Z} /p\mathbb {Z} )^{*}\}=\{\sigma _{a}|a\in (1,\ldots ,(p-1))\}}$ ${\displaystyle \mathbb {Q} (\zeta _{p})}$ ${\displaystyle I}$ ${\displaystyle \mathbb {Z} (\zeta _{p})}$ ${\displaystyle S}$ ${\displaystyle I}$ ${\displaystyle \mathbb {Q} (\zeta _{p})}$ ${\displaystyle S}$

${\displaystyle \theta ={\frac {1}{p}}\sum _{a\in (\mathbb {Z} /p\mathbb {Z} )^{*}}a\sigma _{a}^{-1}}$

from that in is (that is, there is a so ). ${\displaystyle \mathbb {Q} [G]}$ ${\displaystyle \mathbb {Z} [G]}$ ${\displaystyle \beta \in \mathbb {Z} [G]}$ ${\displaystyle S=\beta \theta \in \mathbb {Z} [G]}$

Stickelberger is buried in Freiburg. He had been married since 1895 and had a son who, like his wife, died before him in 1918.

Heinrich Kapferer and the later German Chancellor Joseph Wirth are among his doctoral students .

Web links

• Fritz Nagel: Stickelberger, Ludwig. In: Historical Lexicon of Switzerland .
• Lothar Heffter: Ludwig Stickelberger. Annual report DMV.
• Ludwig Stickelberger: About a generalization of circle healing. Mathematische Annalen 37 (1890), pp. 321-367.
• Boas Erez: Representations of groups in algebraic number theory. An introduction. (PDF; 222 kB).

Individual evidence

1. ^ ^{A b} Ludwig Stickelberger in the Mathematics Genealogy Project
2. ^ List of members Leopoldina, Ludwig Stickelberger
3. ^ Gabriele Dörflinger: Mathematics in the Heidelberg Academy of Sciences. 2014, pp. 78–80.