Denominator-preserving maps

Details Denominator-preserving maps Denominator-preserving maps

2011-03-28

arxiv.org/abs/1103.5473v2

Mathematics

Number Theory

11 pages, 1 figure

Scientific paper

Let F be a continuous injective map from an open subset of R^n to R^n. Assume
that, for infinitely many k>1, F induces a bijection between the rational
points of denominator k in the domain and those in the image (the denominator
of (a_1/b_1,...,a_n/b_n) being the l.c.m. of b_1,...,b_n). Then F preserves the
Lebesgue measure.

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