Nesterenko's criterion when the small linear forms oscillate

Details Nesterenko's criterion when the small linear forms oscillate Nesterenko's criterion when the small linear forms oscillate

2012-01-12

arxiv.org/abs/1201.2651v1

Mathematics

Number Theory

To appear in Archiv der Math

Scientific paper

In this paper we generalize Nesterenko's criterion to the case where the small linear forms have an oscillating behaviour (for instance given by the saddle point method). This criterion provides both a lower bound for the dimension of the vector space spanned over the rationals by a family of real numbers, and a measure of simultaneous approximation to these numbers (namely, an upper bound for the irrationality exponent if 1 and only one other number are involved). As an application, we prove an explicit measure of simultaneous approximation to $\zeta(5)$, $\zeta(7)$, $\zeta(9)$, and $\zeta(11)$, using Zudilin's proof that at least one of these numbers is irrational.

Affiliated with

Also associated with

No associations

Rating

Nesterenko's criterion when the small linear forms oscillate 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 Nesterenko's criterion when the small linear forms oscillate, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nesterenko's criterion when the small linear forms oscillate will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-153324