Guido Hoheisel

Guido Hoheisel (1930)

Guido Kark Heinrich Hoheisel (14 July 1894 – 11 October 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(x) 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.

Hoheisel contributed to the journal Deutsche Mathematik.

During World War II Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster.^[3] His doctoral students include Arnold Schönhage.

Selected works

• Gewöhnliche Differentialgleichungen 1926;^[4] 2nd edition 1930;^[5] 7th edition 1965
• Partielle Differentialgleichungen 1928; 3rd edition 1953
• Aufgabensammlung zu den gewöhnlichen und partiellen Differentialgleichungen 1933^[6]
• Integralgleichungen 1936;^[7] revised and expanded 2nd edition 1963
• Existenz von Eigenwerten und Vollständigkeitskriterium 1943
• Integral equations translated by A. Mary Tropper [1968, c1967]

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.
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.