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 (1777â ...
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