Hans Rademacher

Hans Adolph Rademacher (born April 3, 1892 in Wandsbek , † February 7, 1969 in Haverford , Pennsylvania , United States ) was a German mathematician .

Life

He was one of three children of a shopkeeper in Wandsbek near Hamburg (now part of Hamburg). Rademacher studied from 1910 to 1915 in Göttingen a. a. with Erich Hecke , Hermann Weyl , Edmund Landau and Richard Courant . In 1916 he received his doctorate from Carathéodory with the dissertation Unique images and measurability . In 1919 he completed his habilitation in Berlin, where he also worked as a teacher. In 1922 he became an associate professor in Hamburg and finally in 1925 a full professor in Breslau. In 1933 Rademacher fled as a staunch pacifist and peace activist from the National Socialists to the USA, where he worked as a professor at the University of Pennsylvania in Philadelphia from 1934 , interrupted by numerous visiting professorships, e. B. 1953 at the Institute for Advanced Study in Princeton and in the two following years in Göttingen and at the Tata Institute for fundamental research in Bombay. After his retirement in 1962, he taught at New York University and Rockefeller University in New York.

Rademacher mainly worked in the field of number theory , and here especially in analytical number theory and its connection to the theory of modular forms and its application to combinatorial questions. In 1936 he gave an asymptotic formula for the number of disintegrations (partitions). He also worked on sieving methods and the Goldbach problem . He also found a three-term generalization of the reciprocity formula for Dedekind sums . But he was also very productive in other areas, for example in real analysis , geometry , numerical mathematics , topology and function theory . A system of orthogonal functions introduced by him in 1922, the Rademacher functions , is named after him.

Together with Otto Toeplitz, he is the author of the popular Introduction to the Mathematics of Numbers and Figures.

Rademacher was married several times. From his first marriage, which was divorced in 1929, he had a daughter Karin. From his second marriage, which lasted until 1947, he had a son Peter. His third marriage was from 1949 to the concert pianist Irma Wolpe .

In 1950 he was invited speaker at the International Congress of Mathematicians (ICM) in Cambridge (Massachusetts) (Remarks on the theory of partitions).

His doctoral students include George Andrews , Emil Grosswald , Theodor Estermann , Joseph Lehner and Paul Bateman .

See also

• Rademacher distribution

Fonts

• Some theorems on series of general orthogonal functions . In: Mathematical Annals . Volume 87, 1922, pp. 112-138
• About an extension of Goldbach's problem . In: Mathematical Journal . Volume 25, 1926, pp. 627-657
• with Otto Toeplitz : Of Numbers and Figures. 1930; 2nd edition 1933; Springer 2001, ISBN 3-540-63303-0 .
• with Ernst Steinitz lectures on the theory of the polyhedron including the elements of topology. Springer 1932; 1976 ( online ).
• Generalization of the Reciprocity Formula for Dedekind Sums. In: Duke Math. Journal. Volume 21, 1954, pp. 391-397.
• Lectures on analytic number theory. 1955.
• Lectures on elementary number theory. Blaisdell, New York 1964; Warrior, 1977.
• with Grosswald: Dedekind sums. Carus Mathematical Monographs, 1972.
• Topics in analytic number theory. Edited by Grosswald. Springer Verlag, 1973 (Basic Teachings of the Mathematical Sciences).
• Collected papers. 2 volumes. Edited by Grosswald. MIT press, 1974.
• Higher mathematics from an elementary point of view. Birkhäuser, 1983.

literature

• Rudolf Fritsch :  Rademacher, Hans Adolph. In: New German Biography (NDB). Volume 21, Duncker & Humblot, Berlin 2003, ISBN 3-428-11202-4 , p. 91 f. ( Digitized version ).
• George Andrews, Bressoud, Parsons (Eds.) The Rademacher legacy in mathematics. American Mathematical Society, 1994.
• Lexicon of important mathematicians. German, Thun, Frankfurt am Main, ISBN 3-8171-1164-9 .
• Tom Apostol : Introduction to Analytical number theory. Jumper
• Tom Apostol: Modular functions and Dirichlet Series in Number Theory. Springer (deals with Rademacher's theorem about the disintegration function).

Web links

• Literature by and about Hans Rademacher in the catalog of the German National Library

Footnotes

1. ↑ Hans Adolph Rademacher in the Mathematics Genealogy Project (English)
2. ^ John J. O'Connor, Edmund F. Robertson :  Hans Rademacher. In: MacTutor History of Mathematics archive .
3. ^ Obituary by Berndt in Acta Arithmetica 1992 (PDF; 216 kB)