Guido Hoheisel
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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
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