Guido Hoheisel

Guido Karl Heinrich Hoheisel (* July 14, 1894 in Breslau, † October 11, 1968 in Cologne ) was a German mathematician.

Hoheisel studied from 1914 at the University of Breslau, and from 1920 at the Humboldt University of Berlin, where he received his doctorate in 1920 at Erhard Schmidt ( Linear functional differential equations, Mathematische Zeitschrift Bd.14, 1922, pp.35- 98) and Isay Schur. During his studies he became a member of KStV Unitas Wroclaw. He habilitated in Breslau, where he was a lecturer from 1922 and 1928 associate professor. From 1935 he was in the same capacity at the University of Greifswald and first since 1938 visiting professor and from 1939 full professor at the University of Cologne in 1940 as director of the Mathematical Institute. In 1962, he retired in Cologne.

In 1930 he proved a theorem about prime gaps: if pn is the nth prime, then applies

With a constant θ <1 for sufficiently large n Hoheisel showed that one can take θ = 32999/33000. Further evidence and a tightening of θ = 249/250 gave Hans Heilbronn. Further tightening of the lower limits of θ gave Nikolai Grigoryevich Tschudakow ( Chudakov ) (lower limit ¾ ) in 1936 and Albert Ingham (lower limit 5/8) in 1937 and Martin Huxley 1972 ( θ = 7 /12).

Writings

• Ordinary differential equations, de Gruyter, Sammlung Goschen, 7th, edition 1965
• Partial Differential Equations, de Gruyter, Sammlung Goschen, 1928, 3rd edition 1953
• Integral equations, de Gruyter, Sammlung Goschen, 2nd edition 1963