Hendrik Kloosterman

Hendrik Douwe Kloosterman (born April 9, 1900 in Rottevalle , Netherlands , † May 6, 1968 in Leiden ) was a Dutch mathematician .

Live and act

Hendrik Kloosterman attended school in The Hague and studied mathematics at the University of Leiden , where he received his diploma in 1922. In 1924 he received his doctorate with Jan Cornelis Kluyver in Leiden, after spending some time with Harald Bohr in Copenhagen and Godfrey Harold Hardy at Oxford University on the mediation of Paul Ehrenfest . In his dissertation he investigated the asymptotic number of solutions of a positively definite square form (in diagonal form) in more than five variables. He used the Hardy-Littlewood circle method. Since this was not applicable to the case of four variables (which Joseph-Louis Lagrange already solved), this led to follow-up work in the Acta Mathematica of 1926, in which he introduced his Kloosterman sums, special trigonometric sums that have numerous applications found in analytical number theory and the theory of modular forms and significantly expanded the Hardy-Littlewood method. In 1926/27 he was on a Rockefeller scholarship at the University of Göttingen and in 1927/28 in Hamburg with Erich Hecke , where he applied his method to the determination of the Fourier coefficients of modular shapes. From 1928 he was an assistant at the Westphalian Wilhelms University in Münster , and then in 1930 he became an associate professor (Lector) at the University of Leiden. During the war, when his university was closed, he worked on representations of finite subsets of the module group in the theta functions. From 1947 he was a professor in Leiden.

Since 1950 he has been a member of the Royal Netherlands Academy of Sciences . In 1950 he was invited speaker at the International Congress of Mathematicians (ICM) in Cambridge (Massachusetts) (The characters of binary modular congruence groups).

His PhD students include Jacob Murre and Tonny Albert Springer .

literature

Springer "Kloosterman and his work", Notices AMS 2000, PDF file

Web links

References

^ On the representation of numbers in the form . ${\ displaystyle ay ^ {2} + by ^ {2} + cz ^ {2} + dt ^ {2}}$ Acta Mathematica Vol. 49, 1926, pp. 407-464.
↑ after Peter Sarnak “Bessel functions” finite bodies
^ The behavior of general Theta Functions under the Modular Group and the characters of binary modular subgroups. Annals of Mathematics 1946. The Characters of binary modular congruence subgroups. International Congress of Mathematicians 1950, Cambridge 1952.

personal data
SURNAME	Kloosterman, Hendrik
ALTERNATIVE NAMES	Kloosterman, Hendrik Douwe (full name)
BRIEF DESCRIPTION	Dutch mathematician
DATE OF BIRTH	April 9, 1900
PLACE OF BIRTH	Rottevalle , Netherlands
DATE OF DEATH	May 6, 1968
Place of death	Suffer

[1] On the representation of numbers in the form . ${\ displaystyle ay ^ {2} + by ^ {2} + cz ^ {2} + dt ^ {2}}$ Acta Mathematica Vol. 49, 1926, pp. 407-464.

[2] ter Peter Sarnak “Bessel functions” finite bodies

[3] The behavior of general Theta Functions under the Modular Group and the characters of binary modular subgroups. Annals of Mathematics 1946. The Characters of binary modular congruence subgroups. International Congress of Mathematicians 1950, Cambridge 1952.