Guido Hoheisel

Guido Hoheisel (1930)

Guido Hoheisel (1894–1968) was a German mathematician, a professor of mathematics at the University of Cologne. He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt.^[1]

Hoheisel is known for a result on gaps between prime numbers.^[2] He proved that if π denotes the prime-counting function, then there exists a constant θ < 1 such that

π(x + x^θ) − π(x) ~ x^θ/log(x),

as x tends to infinity, implying that if p_n denotes the n-th prime number then

p_n+1 − p_n < p_n^θ

for all sufficiently large n. In fact he showed that one may take θ = 32999/33000.

During World War II, as one of the few remaining competent mathematicians in Germany, Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster.^[3] His doctoral students include Arnold Schönhage.

References

1. ↑ Guido Hoheisel at the Mathematics Genealogy Project.
2. ↑ G. Hoheisel, Primzahlprobleme in der Analysis, Berliner Sitzungsberichte, pages 580-588, (1930)
3. ↑ Segal, Sanford L. (2003), Mathematicians under the Nazis, Princeton University Press, p. 210, ISBN 978-0-691-00451-8 .