noun
Meaning 1
The subbranch of number theory which applies techniques from geometry to the study of algebraic numbers.
Definition source: English Wiktionary via Wiktextract
Usage: uncountable
Topics: mathematics, number-theory, sciences
Examples
- A typical approach in the geometry of numbers is to view a ring of algebraic integers as a lattice in #92;textstyle#92;mathbb#123;R#125;n; 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 n-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 α1x_1+...+αnx_n(mod 1)|x_i=0,...N, or by geometry of numbers by applying Minkowski's first theorem in C.2.19 to the symmetric convex body of volume 2n+1 given by |X_0+α1X_1+...αnX_n|<N−n,|X_i|<N,i=1,...N.
Meaning relationships
Synonyms: none provided
Antonyms: none provided