Titlebook: Lectures on the Geometry of Numbers; Carl Ludwig Siegel,Komaravolu Chandrasekharan Book 1989 Springer-Verlag Berlin Heidelberg 1989 Volume

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Lecture IIIWe proved in Lecture II that if .. is defined by . then it is an even gauge function on ℝ.. In this section we shall evaluate the integral for the volume .. of the convex body ..defined by . We have

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Lecture IVLet . be an even gauge function on ℝ., and . the convex body defined by {.| . (.) < 1}. Let ..,..., .. be the . of ., and let the minima be attained at the vectors ..,..., .., called the .. Another way of looking at this fact is as follows:

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Lecture VIThe preceding lecture has shown that in any discrete vector group . of rank r, there exists a basis, that is r linearly independent vectors ..,..., .. ,such that any vector . belonging to . can be written as.where ..,..., .. are integers.

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Lecture VIIWe shall use our results about the decomposition of vector groups to discuss the possible number of periods of real and complex functions.

Cardioplegia

Lecture IXConsider the following . linear forms with real coefficients.where the matrix (a.), ., . = 1,…, ., is non-singular, and let . = |det(a.)|.

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Lecture XIn the two previous lectures we have obtained theorems about the minima of quadratic forms on the set of all non-zero integral points. These theorems can be formulated in terms of lattices. For example, the theorem about the minimum of positive-definite binary quadratic forms gives the following result:

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