Guido Hoheisel

Guido Hoheisel (1930)

Guido Karl Heinrich Hoheisel (14 July 1894 – 11 October 1968) was a German mathematician and professor of mathematics at the University of Cologne.

Academic life

He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt. During World War II Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster. His doctoral students include Arnold Schönhage.

Hoheisel contributed to the journal Deutsche Mathematik.

Selected results

Hoheisel is known for a result on gaps between prime numbers: He proved that if π(x) denotes the prime-counting function, then there exists a constant θ < 1 such that

π(x + xθ) − π(x) ~ xθ/log(x),

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

pn+1 − pn < pnθ,

for all sufficiently large n. He showed that one may take

θ = 32999/33000 = 1 - 0.000(03),

with (03) denoting periodic repetition.

Selected works

References

  1. ↑ Guido Hoheisel at the Mathematics Genealogy Project.
  2. ↑ Segal, Sanford L. (2003), Mathematicians under the Nazis, Princeton University Press, p. 210, ISBN 978-0-691-00451-8.
  3. ↑ G. Hoheisel, Primzahlprobleme in der Analysis, Berliner Sitzungsberichte, pages 580-588, (1930)
  4. ↑ Cohen, A. (1929). "Review: Gewöhnliche Differentialgleichungen by G. Hoheisel" (PDF). Bull. Amer. Math. Soc. 35 (1): 136–137. doi:10.1090/s0002-9904-1929-04716-5.
  5. ↑ Longley, W. R. (1932). "Review: Gewöhnliche Differentialgleichungen by G. Hoheisel" (PDF). Bull. Amer. Math. Soc. 38 (7): 478–479. doi:10.1090/s0002-9904-1932-05447-7.
  6. ↑ Longley, W. R. (1933). "Review: Aufgabensammlung zu den gewöhnlichen und partiellen Differentialgleichungen by G. Hoheisel" (PDF). Bull. Amer. Math. Soc. 39 (9): 652–653. doi:10.1090/s0002-9904-1933-05695-1.
  7. ↑ Longley, W. R. (1937). "Review: Integralgleichungen by G. Hoheisel" (PDF). Bull. Amer. Math. Soc. 43 (1): 14–15. doi:10.1090/s0002-9904-1937-06480-9.