The quantitative behaviour of polynomial orbits on nilmanifolds

Details The quantitative behaviour of polynomial orbits on nilmanifolds The quantitative behaviour of polynomial orbits on nilmanifolds

2007-09-22

arxiv.org/abs/0709.3562v5

Mathematics

Number Theory

62 pages, to appear in Annals of Math. Small changes made in the light of comments from the referee.

Scientific paper

A theorem of Leibman asserts that a polynomial orbit (g(1),g(2),g(3),...) on a nilmanifold G/L is always equidistributed in a union of closed sub-nilmanifolds of G/L. In this paper we give a quantitative version of Leibman's result, describing the uniform distribution properties of a finite polynomial orbit (g(1),...,g(N)) in a nilmanifold. More specifically we show that there is a factorization g = eg'p, where e(n) is "smooth", p(n) is periodic and "rational", and (g'(a),g'(a+d),...,g'(a + d(l-1))) is uniformly distributed (up to a specified error delta) inside some subnilmanifold G'/L' of G/L, for all sufficiently dense arithmetic progressions a,a+d,...,a+d(l-1) inside {1,..,N}. Our bounds are uniform in N and are polynomial in the error tolerance delta. In a subsequent paper we shall use this theorem to establish the Mobius and Nilsequences conjecture from our earlier paper "Linear equations in primes".

Affiliated with

Also associated with

No associations

Rating

The quantitative behaviour of polynomial orbits on nilmanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The quantitative behaviour of polynomial orbits on nilmanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The quantitative behaviour of polynomial orbits on nilmanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-543994