Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nesterenko's criterion when the small linear forms oscillate   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.

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The categories of this paper are: nlin
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org