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
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 ...
, 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