Helmut Brückner (mathematician)

Helmut Brückner (born April 13, 1938 in Bremen ) is a German mathematician who deals with algebraic number theory.

Brückner studied mathematics, physics, philosophy and pedagogy at the University of Hamburg from 1957 to 1962 , passed his teaching examination in 1963 and received his doctorate there in 1964 under Helmut Hasse (An explicit formula for the p-th standard symbol in discreetly valued complete bodies of the characteristic 0 with a complete residual class field the characteristic p). He was a professor at the University of Hamburg, where he has now retired.

In the 1960s, Brückner demonstrated the validity of the general law of reciprocity for nth power residues by explicitly calculating the norm residue symbols. Igor Schafarewitsch (1950s) and Sergei Vladimirovich Vostokow (1978) in Russia also independently investigated explicit reciprocity laws . This provided a concretization and a certain conclusion in the theory of the general laws of reciprocity, a central topic of algebraic number theory that goes back to Legendre and Gauß ( square reciprocity law , Gauß's first higher reciprocity laws) and its story then about Eisenstein , Ernst Eduard Kummer , David Hilbert (who put the general reciprocity law for nth power residues as the ninth of the Hilbert problems ), Teiji Takagi , Philipp Furtwängler up to Emil Artin and Hasse. The search for and the proof of more and more general formulations of the reciprocity law was one of the driving forces behind the development of algebraic number theory (emergence of the class field theory ).

His doctoral students include Uwe Jannsen and Kay Wingberg .

Fonts

• Explicit Reciprocity Law and Applications, Lecture Development, University of Essen, 1979
• An explicit formula for the reciprocity law for prime exponents p in Algebraic Number Theory, in Algebraic Number Theory (Oberwolfach), BI University Pocket Books 1967, pp. 31-39

Web links

• Homepage at the University of Hamburg