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On a class of numbers generated by differencial equations related with algebraic groups

Published online by Cambridge University Press:  22 January 2016

Hiroshi Umemura
Hiroshi Umemura*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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In this paper we propose a new category Qcl of complex numbers which contains π, e and the set of algebraic numbers. In fact this category contains most of the numbers studied so far in number theory. An element of the category is here called a classical number. The category of the classical numbers forms an algebraically closed field and consists of countably many numbers. The definition depends on algebraic differential equations related with algebraic groups. Throughout the paper unless otherwise stated, we deal with functions of one variable and a differential equation is an ordinary differential equation. We are inspired of the Leçons de Stockholm of Painlevé [P].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 133 , March 1994 , pp. 1 - 55
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

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