Hans-Egon Richert

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Hans-Egon Richert
Born ( 1924 -06-02)June 2, 1924
Hamburg, Germany
Died November 25, 1993( 1993 -11-25)
Blaustein, Germany
Residence Germany
Fields Mathematics
Institutions University of Göttingen
University of Marburg
University of Ulm
Alma mater University of Hamburg
Doctoral advisor Max Deuring
Known for additive number theory
sieve theory
Dirichlet divisor problem

Hans-Egon Richert (June 2, 1924 – November 25, 1993) was a German mathematician who worked primarily in analytic number theory. He is the author (with Heini Halberstam) of a definitive book[1] on sieve theory.

Life and education[edit]

Hans-Egon Richert was born in 1924 in Hamburg, Germany. He attended the University of Hamburg and received his Ph.D under Max Deuring in 1950. He held a temporary chair at the University of Göttingen and then a newly created chair at the University of Marburg. In 1972 he moved to the University of Ulm, where he remained until his retirement in 1991. He died on November 25, 1993 in Blaustein, near Ulm, Germany.[2]

Work[edit]

Richert worked primarily in analytic number theory, and beginning around 1965 started a collaboration with Heini Halberstam and shifted his focus to sieve theory. For many years he was a chairman of the Analytic Number Theory meetings at the Mathematical Research Institute of Oberwolfach.[2]

Analytic number theory[edit]

Richert made contributions to additive number theory, Dirichlet series, Riesz summability, the multiplicative analog of the Erdős–Fuchs theorem, estimates of the number of non-isomorphic abelian groups, and bounds for exponential sums. He proved the exponent 15/46 for the Dirichlet divisor problem, a record that stood for many years.[2]

Sieve methods[edit]

One of Richert's notable results was the Jurkat–Richert theorem, joint work with Wolfgang B. Jurkat that improved the Selberg sieve and is used in the proof of Chen's theorem.[3]:257 Richert also produced a "readable form"[2] of Chen's theorem (it is covered in the last chapter of Sieve Methods[1]).

Halberstam & Richert's book Sieve Methods[1] was the first exhaustive account of the subject. [4] In reviewing the book in 1976, Hugh Montgomery wrote "In the past, researchers have generally derived the sieve bounds required for an application, but now workers will find that usually an appeal to an appropriate theorem of Sieve methods will suffice," and "For years to come, Sieve methods will be vital to those seeking to work in the subject, and also to those seeking to make applications."[4]

Notes[edit]

  1. ^ a b c Halberstam, Heini; H. E. Richert (1974). Sieve Methods. London: Academic Press. ISBN 0-12-318250-6. MR 54:12689. Halberstam, Heini; Richert, Hans-Egon (2011). Sieve Methods (2nd ed.). Dover. ISBN 0-486-47939-0. 
  2. ^ a b c d Vorhauer, Ulrike; Eduard Wirsing (January 1994). "Died: Prof. Dr. Hans-Egon Richert". University of Ulm. Retrieved 2008-07-21. 
  3. ^ Nathanson, Melvyn (1996). Additive Number Theory: The Classical Bases. Berlin: Springer. ISBN 0-387-94656-X. 
  4. ^ a b Montgomery, H. L. (November 1976). "Book Reviews: Sieve Methods". Bulletin of the American Mathematical Society (Providence: American Mathematical Society) 82 (6): 846–853. doi:10.1090/S0002-9904-1976-14180-8. 

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