Guido_Hoheisel
Guido Karl Heinrich Hoheisel (14 July 1894 – 11 October 1968) was a German mathematician and 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] During World War II Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster.[2] His doctoral students include Arnold Schönhage.
Hoheisel contributed to the journal Deutsche Mathematik.
Hoheisel is known for a result on gaps between prime numbers:[3] 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.
- 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]
- Segal, Sanford L. (2003), Mathematicians under the Nazis, Princeton University Press, p. 210, ISBN 978-0-691-00451-8.
- G. Hoheisel, Primzahlprobleme in der Analysis, Berliner Sitzungsberichte, pages 580-588, (1930)
- 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.
- 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.
- 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.
- 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.