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I was wondering if someone would be willing to suggest an alternative reference to Davenport's book Analytic Methods for Diophantine Equations and Diophantine Equations. I like the book but I would like to read up from a different source some theorems about the geometry of numbers which are important to analytic number theorists. I apologize if the question is too broad. Thanks!

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    $\begingroup$ Cassels 'Introduction to the Geometry of Numbers' is the classical reference for this area. Or, depending what you're looking for, chaper 2 of Tao and Vu's 'Additive Combinatorics' might be a more modern treatment. It's also worth looking at Vaughan's 'Hardy-Littlewood Method' for more on the circle method. $\endgroup$
    – Thomas Bloom
    Commented Oct 24, 2019 at 18:07
  • $\begingroup$ Ah, I see. I shall check these out, especially Cassels. However, I think Vaughan doesn't talk about the geometry of numbers. $\endgroup$
    – user147650
    Commented Oct 25, 2019 at 11:25

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Some classical books on the subject, I use them all:

  • Cassels: An introduction to the geometry of numbers
  • Gruber-Lekkerkerker: Geometry of numbers
  • Siegel-Chandrasekharan: Lectures on the geometry of numbers
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    $\begingroup$ Thank you so much for the list of references. I found the third one particularly well-motivated. Also, Taylor and Fröhlich's Algebraic Number Theory also had a few things that I was looking for in geometry of numbers (removed previous comment about Cassels and Fröhlich which is a different text). $\endgroup$
    – user147650
    Commented Feb 2, 2020 at 22:05

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