Titlebook: Lecture Notes on Geometry of Numbers; R. J. Hans-Gill,Madhu Raka,Ranjeet Sehmi Textbook 2024 The Editor(s) (if applicable) and The Author(

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,Minkowski’s Fundamental Theorem and Its Applications,m of linear forms and give its application to simultaneous approximation of reals by rationals. We briefly define lattices and then prove Minkowski’s Fundamental Theorem for lattices. Generalizations of Minkowski’s Fundamental Theorem by Blichfeldt and Van der Corput are also given.

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Minima of Positive Definite Quadratic Forms,inkowski’s Fundamental Theorem. In this chapter, we give a proof of Hermite’s inequality .. We also give a proof of Mordell’s result .. Further, we obtain . for . and 3. As an application, we derive necessary and sufficient conditions for a positive integer to be a sum of . squares for ..