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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.〔.〕 Hoheisel is known for a result on gaps between prime numbers.〔G. Hoheisel, ''Primzahlprobleme in der Analysis'', Berliner Sitzungsberichte, pages 580-588, (1930)〕 He proved that if π(x) denotes the prime-counting function, then there exists a constant θ < 1 such that :π(''x'' + ''x''θ) − π(''x'') ~ ''x''θ/log(''x''), as ''x'' tends to infinity, implying that if ''p''''n'' denotes the ''n''-th prime number then :''p''''n''+1 − ''p''''n'' < ''p''''n''''θ'' for all sufficiently large ''n''. In fact he showed that one may take θ = 32999/33000. Hoheisel contributed to the journal Deutsche Mathematik. 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. == 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 (c1967 ) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Guido Hoheisel」の詳細全文を読む スポンサード リンク
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