Lattices: Properties and Theta Functions

In course

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Description

This lecture introduces the concept of lattices in Rd as discrete abelian subgroups, exploring examples and properties such as Gram matrices and dual lattices. The instructor discusses theta functions, their Fourier transforms, and the Poisson summation formula, emphasizing modular properties and transformation laws. The lecture concludes with the analysis of theta functions' growth and the existence of even unimodular lattices in higher dimensions.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_zswiq642

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra, Abstract algebra

Number theory: Topics in number theory

Information engineering

Signal processing: Fourier analysis

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