Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pad\'e approximation for a class of hypergeometric functions and
  parametric geometry of numbers   In this article we obtain new irrationality measures for values of functions
which belong to a certain class of hypergeometric functions including shifted
logarithmic functions, binomial functions and shifted exponential functions. We
explicitly construct Pad\'e approximations by using a formal method and show
that the associated sequences satisfy a Poincar\'e-type recurrence. To study
precisely the asymptotic behavior of those sequences, we establish an
\emph{effective} version of the Poincar\'e-Perron theorem. As a consequence we
obtain, among others, effective irrationality measures for values of binomial
functions at rational numbers, which might have useful arithmetic applications.
A general theorem on simultaneous rational approximations that we need is
proven by using new arguments relying on parametric geometry of numbers.

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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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
11
The categories of this paper are: hep-lat