- Source: 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.
Academic life
He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt.
During World War II Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster. 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:
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; 2nd edition 1930; 7th edition 1965
Partielle Differentialgleichungen 1928; 3rd edition 1953
Aufgabensammlung zu den gewöhnlichen und partiellen Differentialgleichungen 1933
Integralgleichungen 1936; revised and expanded 2nd edition 1963
Existenz von Eigenwerten und Vollständigkeitskriterium 1943
Integral equations translated by A. Mary Tropper [1968, c1967]