geometry of numbers

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English

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English Wikipedia has an article on:
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Etymology

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The field was initiated by German mathematician Hermann Minkowski (1910, Geometrie der Zahlen).

Noun

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geometry of numbers (uncountable)

  1. (number theory) The subbranch of number theory which applies techniques from geometry to the study of algebraic numbers.
    A typical approach in the geometry of numbers is to view a ring of algebraic integers as a lattice in ; the study of these lattices provides fundamental information on algebraic numbers.
    • 1969, C. G. Lekkerkerker, Geometry of Numbers, Wolters-Noordoff, North-Holland, page 1,
      The geometry of numbers to which this book is devoted deals with arbitrary bodies and arbitrary lattices in the -dimensional euclidean space. Its aim is to study various quantities describing the behaviour of a body with respect to a lattice.
    • 2006, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 181,
      The easy proof is obtained applying the pigeon-hole principle to
      ,
      or by geometry of numbers by applying Minkowski's first theorem in C.2.19 to the symmetric convex body of volume given by
      .

Translations

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Further reading

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