Johannes van der Corput

Johannes Gualtherus van der Corput (born September 4, 1890 in Rotterdam , † September 16, 1975 in Amsterdam ) was a Dutch mathematician who dealt with analytical number theory and analysis .

Life

Van der Corput studied from 1908 to 1914 at the University of Leiden , among others with the number theorist Jan Cornelis Kluyver. During the First World War he served as an officer and from 1917 was a teacher in Leeuwarden and Utrecht. At the same time he did his doctorate in Leiden in analytical number theory (the dissertation was published in Groningen in 1919 On grid points in the plane , Over roosterpunten in het platte vlak ). In 1920 he was with Edmund Landau in Göttingen , from 1920 to 1922 assistant to Arnaud Denjoy at the University of Utrecht , in 1922 professor at the University of Friborg in Switzerland and from 1923 professor in Groningen . From 1945 to 1953 he was a professor at the University of Amsterdam . He was a co-founder of the Mathematical Center (today Centrum Wiskunde & Informatica ) in Amsterdam and was its first director from 1946 to 1953. In 1953 he went to the USA: to the University of California, Berkeley and the University of Wisconsin – Madison .

Until 1940 he dealt almost exclusively with analytical number theory (among other things with the following topics: distribution of grid points, Winogradow's methods for estimating exponential sums, geometry of numbers , Goldbach conjecture , Diophantine approximation , order of the growth of the Riemann zeta function ), then also with other math problems. For example, he published a new proof of the fundamental theorem of algebra and he helped popularize the elementary proof of the prime number theorem by Paul Erdős and Atle Selberg .

In 1922 he proved ( tightening of the estimation in the case of the divider problem , Mathematische Annalen, vol. 87 1922, p. 39) that the number of integer grid points N in a circle with a radius is asymptotic ${\ displaystyle {\ sqrt {x}}}$

{\ displaystyle \, N (x) = \ pi x + O (x ^ {\ theta})}

is for a constant . Until then, 1/3 was considered to be a lower limit of the exponent in the asymptotic residual term (the lower limit of ¼ was already proven in 1915 by Godfrey Harold Hardy and Edmund Landau ). He gave a similar estimate for the asymptotic residual term of the number function . ${\ displaystyle \ theta <{\ frac {1} {3}}}$

In 1929 he became a member of the Royal Netherlands Academy of Sciences and he was also a member of the Royal Belgian Academy of Sciences and honorary doctorates from Bordeaux and Delft. In 1936 he gave a plenary lecture at the International Congress of Mathematicians in Oslo (Diophantine Approximations).

His students included Jurjen Koksma , Lubbertus Nieland, Jan Popken, Cornelis Simon Meijer and Barend Meulenbeld.

Web links

Individual evidence

↑ See also the article Some problems in number theory I: The Circle Problem by Sylvain Cappell and Julius Shaneson ( arxiv : math / 0702613 ), in which the bound O ( x 1/4 ^{+ ε} ) is derived (correctness of the proof still unclear - As of May 2010).

personal data
SURNAME	Corput, Johannes van der
ALTERNATIVE NAMES	Corput, Johannes Gualtherus van der (full name)
BRIEF DESCRIPTION	Dutch mathematician
DATE OF BIRTH	September 4, 1890
PLACE OF BIRTH	Rotterdam
DATE OF DEATH	16th September 1975
Place of death	Amsterdam

[1] See also the article Some problems in number theory I: The Circle Problem by Sylvain Cappell and Julius Shaneson ( arxiv : math / 0702613 ), in which the bound O ( x 1/4 ^{+ ε} ) is derived (correctness of the proof still unclear - As of May 2010).