Guido Hoheisel

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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.[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.

Selected results

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.

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. ^ 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.
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