geometric number theory

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geometric number theory

[¦jē·ə¦me·trik ′nəm·bər ‚thē·ə·rē]
(mathematics)
The branch of number theory studying relationships among numbers by examining the geometric properties of ordered pair sets of such numbers.
References in periodicals archive ?
The Fields winners were selected for their contributions to topics ranging from dynamical systems to the geometry of numbers and the solution of equations of the type that describe many physical phenomena.
Bhargava, born in 1974 in Canada, was awarded the Fields Medal for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves.
Their topics include divisibility, polynomial congruences, quadratic reciprocity, the geometry of numbers, and algebraic integers.
The book is suitable for researchers and graduate students interested in combinatorial aspects of commutative algebra, optimization, discrete geometry, statistics, mirror symmetry, and geometry of numbers.
The geometry of numbers is illustrated by the following hands-on task using 7 matchsticks or straight rods of equal length.