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On a Principle of Lipschitz
Author(s) -
Davenport H.
Publication year - 1964
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-39.1.580-t
Subject(s) - citation , lipschitz continuity , factorization , mathematics , computer science , mathematical economics , combinatorics , algebra over a field , library science , pure mathematics , algorithm
1. It is often desirable to be able to approximate to the number of points with integral coordinates in a closed bounded region R in n dimensional space by means of the volume V(K) of ft. The position is very simple if R depends on one parameter X, and is obtained froma fixed region r\x by uniform dilatation about the origin with linear ratio of dilatation X. Then it is immediate that the number of points with integral coordinates in ft is