Frits Beukers () (born 1953,

Ankara Ankara ( , ; ), historically known as Ancyra and Angora, is the capital of Turkey. Located in the central part of Anatolia, the city has a population of 5.1 million in its urban center and over 5.7 million in Ankara Province, maki ...

) is a Dutch mathematician, who works on

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and hypergeometric functions. In 1979 Beukers received his PhD at

Leiden University Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...

under the direction of

Robert Tijdeman Robert Tijdeman (born 30 July 1943 in Oostzaan, North Holland) is a Dutch mathematician. Specializing in number theory, he is best known for his Tijdeman's theorem. He is a professor of mathematics at the Leiden University since 1975, and was c ...

with thesis ''The generalized

Ramanujan–Nagell Equation In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be ...

'', published in ''

Acta Arithmetica ''Acta Arithmetica'' is a scientific journal of mathematics publishing papers on number theory. It was established in 1935 by Salomon Lubelski and Arnold Walfisz. The journal is published by the Institute of Mathematics of the Polish Academy of Sc ...

'', vol. 38, 1980/1981. From 1979 to 1980 he was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

.Institute for Advanced Study: A Community of Scholars
/ref> He became a professor in Leiden and in the 2000s at

Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollme ...

. Beukers works on questions of transcendence and

irrationality Irrationality is cognition, thinking, talking, or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. ...

in number theory, and on other topics. In connection with the famous proof by

Roger Apéry Roger Apéry (; 14 November 1916, Rouen – 18 December 1994, Caen) was a French mathematician most remembered for Apéry's theorem, which states that is an irrational number. Here, denotes the Riemann zeta function. Biography Apéry was born ...

(1978) on the irrationality of the values of the

Riemann zeta function The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...

evaluated at the points 2 and 3, Beukers gave a much simpler alternate proof using

Legendre polynomials In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applicat ...

. He also published on questions in mechanics about

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

s and their exact solvability.

Selected works

* * * ''A rational approach to Pi'', Nieuw Archief voor Wiskunde, 2000, Heft 4 *

References

External links

Homepage in Utrecht
* {{DEFAULTSORT:Beukers, Frits 1953 births Living people 20th-century Dutch mathematicians 21st-century Dutch mathematicians Leiden University alumni Academic staff of Leiden University Academic staff of Utrecht University Institute for Advanced Study visiting scholars People from Ankara