Arnold Scholz

Arnold Scholz (born December 24, 1904 in Charlottenburg , † February 1, 1942 in Flensburg ) was a German mathematician who dealt with algebraic number theory.

Live and act

Scholz was the son of Reinhold Scholz (Head of Department at the Military Experimental Office), attended the Kaiserin Auguste Gymnasium in Charlottenburg and studied mathematics, philosophy and musicology at the University of Berlin from 1923 to 1928 . a. with Issai Schur , with whom he received his doctorate “magna cum laude” in 1928 (On the formation of algebraic number fields with a resolvable Galois group, Mathematische Zeitschrift Vol. 30, 1929, p. 332). In 1927 he spent a semester in Vienna with Philipp Furtwängler . After completing his doctorate, he was an assistant in Berlin and from 1930 private lecturer in Freiburg im Breisgau . From 1935 to 1940 he had a teaching position at the University of Kiel , where he completed his habilitation in 1934 and was then a lecturer. In 1940 he was drafted and was a mathematics teacher at the Naval Academy in Flensburg - Mürwik . From his student days until his death he was in lively correspondence with Helmut Hasse and worked with Olga Taussky-Todd in the 1930s . In 1942 he died of diabetes.

Scholz worked in algebraic number theory. Among other things, he made early work on the inverse problem of Galois theory in algebraic number fields, where he and Hans Reichardt showed the solvability of the problem for p groups (p prim, odd). The work of Reichardt and Scholz was taken up after the war by Igor Schafarewitsch (who showed the solvability for solvable groups). In 1928 Scholz showed the existence of algebraic number fields with a class field tower of any size.

A reciprocity law is named after him (which, after Franz Lemmermeyer, was already known to Theodor Schönemann ).

In his estate there was also an almost completed manuscript Special Numbers for the new edition of the Encyclopedia of Mathematical Sciences .

Fonts

• On the formation of algebraic number fields with a resolvable Galois group, Inaugural dissertation, Berlin 1928 and Mathematische Zeitschrift, vol.30, 1929
• with Helmut Hasse : On the class field theory based on Takagic , Mathematische Zeitschrift 29, 1929, pp. 60–69
• Two observations on the class field tower , Crelles Journal 161, 1929, pp. 201-207
• About the relationship of the class numbers of square bodies to one another , Crelles Journal 166, 1932, pp. 201-203
• About the solvability of the equation t² − Du² = −4 , Mathematische Zeitschrift 39, 1934, pp. 95–111
• with Olga Taussky : The main ideals of the cubic class fields of imaginary-quadratic number fields: their computational determination and their influence on the class field tower , Crelles Journal 171, 1934, pp. 19–41
• The circular class fields of prime power degrees and the construction of fields with a given two-stage group I , Mathematische Annalen Vol. 109, 1934, p. 161, Part 2 , Mathematische Annalen, Vol. 110, 1935, p. 633
• Total remnants of norms, which are not norms, as producers of non-Abelian body extensions. I , Crelles Journal 175, 1936, pp. 100-107
• Construction of algebraic number fields with any group of prime power order. I , Mathematische Zeitschrift 42, 1937, pp. 161-188
• Minimal Discriminants of Algebraic Number Fields , Crelles Journal 179, 1938, pp. 16-21
• Introduction to number theory , Göschen Collection, de Gruyter, Berlin 1939
  • Revised by Bruno Schoeneberg : Introduction to Number Theory (5th edition), de Gruyter, Berlin 1973
• On Abelian Crossing , Crelles Journal 182, 1940, p. 216
• Total remnants of norms, which are not norms, as producers of non-Abelian body extensions. II , Crelles Journal 182, 1940, pp. 217-234
• On the ideal theory in infinite algebraic number fields , Crelles Journal 185, 1943, pp. 113–126

estate

• Special number fields ( DVI file), intended for the encyclopedia of mathematical sciences (unfinished)

literature

• Olga Taussky-Todd : Arnold Scholz on memory ( DVI file), Mathematische Nachrichten 7, 1952, pp. 379–386
• Helmut Hasse, Arnold Scholz, Olga Taussky: The correspondence between Hasse-Scholz-Taussky, ed. by Franz Lemmermeyer and Peter Roquette, Universitätsverlag Göttingen, 2016, doi : 10.17875 / gup2016-909

Web links

• Literature by and about Arnold Scholz in the catalog of the German National Library
• "Gechichtliches" - with a short biography and list of publications
• 1904 - 2004 In memory of the genius Arnold Scholz - with a short biography

Individual evidence

1. ↑ Lemmermeyer reciprocity laws , Springer Verlag, 2000, p. 160