David Hilbert: The theory of algebraic number fields. Jahresber. Deutsche Math. Ver. 4 (1897), 175--546

DOI10.1365/s13291-017-0168-3zbMath1397.01016OpenAlexW2689194049MaRDI QIDQ680847

Franz Lemmermeyer

Publication date: 29 January 2018

Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1365/s13291-017-0168-3

zbMATH Keywords

reciprocity lawalgebraic number fieldsgenus theorylogarithmic derivativefundamental theorem of ideal theoryHilbert norm-residue symbolZahlbericht

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of number theory (11-03) Algebraic numbers; rings of algebraic integers (11R04) History of mathematics in the 19th century (01A55) Power residues, reciprocity (11A15)

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Cites Work

• Emil Artin and Helmut Hasse. The correspondence 1923--1958. Translated from the German by Franz Lemmermeyer
• Number theory of the Greeks. II: Gauss lemmas and Riesz rings
• The Frattini subgroup of a \(p\)-group
• Jacobi and Kummer's ideal numbers
• Primes of degree one and algebraic cases of Čebotarev's theorem
• The background of Kummer's proof of Fermat's last theorem for regular primes
• Euclidean number fields of large degree
• Galois action on class groups
• Reciprocity laws and Galois representations: recent breakthroughs
• On knots in algebraic number theory.
• Cyclotomic Fields and Zeta Values
• Totale Normenreste, die keine Normen sind, als Erzeuger nichtabelscher Körpererweiterungen. II.
• David Hilbert and his mathematical work
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