Lecture III

Carl Ludwig Siegel and Komaravolu Chandrasekharan
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Komaravolu Chandrasekharan: ETH Zürich, Mathematik

A chapter in Lectures on the Geometry of Numbers, 1989, pp 25-32 from Springer

Abstract: Abstract We proved in Lecture II that if f r is defined by 1 $${f_r}\left( x \right) = {\left( {\sum\limits_{j = 1}^n {{{\left| {{x_j}} \right|}^r}} } \right)^{1/r}},{\kern 1pt} {\kern 1pt} x \in {\mathbb{R}^n}{\kern 1pt} ,{\kern 1pt} r \geqslant 1{\kern 1pt} ,$$ then it is an even gauge function on ℝ n . In this section we shall evaluate the integral for the volume V r of the convex body B r defined by $$\left\{ {x\left| {{f_r}\left( x \right)

Date: 1989
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DOI: 10.1007/978-3-662-08287-4_3

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