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Lattices and Modular Forms Metro Luka Supervisor: Graham Ellis August 2022Contents 1 Lattices 1.1 The Sphere Packing Problem. . . . . . . . . . . . . . . . . . 1.2 Lattice Theory Fundamentals. . .
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Understand the basic principles of lattices and modular forms
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Identify the lattice points on a given lattice
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Fill out the lattice by assigning values to the lattice points based on the modular form

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Lattices refer to discrete subgroups of a vector space that form a periodic structure, while modular forms are complex analytic functions that satisfy a certain transformation property under modular group action.
Individuals or organizations involved in mathematical research or relevant fields may be required to file lattices and modular forms.
Lattices and modular forms can be filled out by providing relevant mathematical data and calculations in the designated sections of the form.
Lattices and modular forms are used to study the properties of periodic structures and complex analytic functions for various mathematical applications.
Information such as lattice parameters, transformation properties, and mathematical calculations related to modular forms must be reported on lattices and modular forms.
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