Hans-Egon Richert (June 2, 1924 – November 25, 1993) was a

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

mathematician who worked primarily in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...

. He is the author (with Heini Halberstam) of a definitive book on sieve theory.

Life and education

Hans-Egon Richert was born in 1924 in Hamburg, Germany. He attended the University of Hamburg and received his Ph.D under

Max Deuring Max Deuring (9 December 1907 – 20 December 1984) was a German mathematician. He is known for his work in arithmetic geometry, in particular on elliptic curves in characteristic p. He worked also in analytic number theory. Deuring graduated fr ...

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.

Work

Richert worked primarily in

, 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 The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekl ...

Analytic number theory

Richert made contributions to additive number theory, Dirichlet series, Riesz summability, the multiplicative analog of the

Erdős–Fuchs theorem In mathematics, in the area of additive number theory, the Erdős–Fuchs theorem is a statement about the number of ways that numbers can be represented as a sum of elements of a given additive basis, stating that the average order of this numbe ...

, 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 Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and ...

, a record that stood for many years.

Sieve methods

One of Richert's notable results was the

Jurkat–Richert theorem The Jurkat–Richert theorem is a mathematical theorem in sieve theory. It is a key ingredient in proofs of Chen's theorem on Goldbach's conjecture. It was proved in 1965 by Wolfgang B. Jurkat and Hans-Egon Richert. Statement of the theorem Th ...

, joint work with Wolfgang B. Jurkat that improved the Selberg sieve and is used in the proof of

Chen's theorem In number theory, Chen's theorem states that every sufficiently large parity (mathematics), even number can be written as the sum of either two prime number, primes, or a prime and a semiprime (the product of two primes). History The theorem wa ...

. Richert also produced a "readable form" of Chen's theorem (it is covered in the last chapter of ''Sieve Methods'').

Halberstam Halberstam ( yi, ‎, he, ‎) is a Jewish surname, used by several branches of the Halberstadt family. Halberstam, meaningless in its current form, is altered from an older name, Halberstadt, used by many descendants of Rabbi Tzvi Hirsh (di ...

& Richert's book ''Sieve Methods'' was the first exhaustive account of the subject. 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."

Notes

External links

* {{DEFAULTSORT:Richert, Hans-Egon 1924 births 1993 deaths 20th-century German mathematicians Number theorists University of Hamburg alumni Academic staff of the University of Marburg Academic staff of the University of Ulm