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What are the applications of Geometry of Numbers? I think it proves the following things:

  • Fermat's Christmas Theorem
  • Lagrange 4-square Theorem
  • Finiteness of Class Group
  • Dirichlet's Unit Theorem

would love to hear about more.

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    I fl$a$gged this for community wiki $b$ut please don't make it community wiki I want to accept the notes as an answer.2012-12-11

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Have you reviewed this: http://math.uga.edu/~pete/geometryofnumbers.pdf ?

There are also several books on the topic and a Wiki page with references too.

-A

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    Pete's got a really nice collection of notes (all pdf)...check out his page at the above URL, minus the "geometryofnumbers.pdf"2013-05-15