Guido Hoheisel

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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(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+1pn < pnθ

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.

Selected works[edit]

  • 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[edit]

  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". Bull. Amer. Math. Soc. 35 (1): 136. 
  5. ^ Longley, W. R. (1932). "Review: Gewöhnliche Differentialgleichungen by G. Hoheisel". Bull. Amer. Math. Soc. 38 (7): 478. 
  6. ^ Longley, W. R. (1933). "Review: Aufgabensammlung zu den gewöhnlichen und partiellen Differentialgleichungen by G. Hoheisel". Bull. Amer. Mth. Soc. 39 (9): 652. 
  7. ^ Longley, W. R. (1937). "Review: Integralgleichungen by G. Hoheisel". Bull. Amer. Math. Soc. 43 (1): 14.