Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypertranscendence and linear difference equations   After H\"older proved his classical theorem about the Gamma function, there
has been a whole bunch of results showing that solutions to linear difference
equations tend to be hypertranscendental i.e. they cannot be solution to an
algebraic differential equation). In this paper, we obtain the first complete
results for solutions to general linear difference equations associated with
the shift operator $x\mapsto x+h$ ($h\in\mathbb{C}^*$), the $q$-difference
operator $x\mapsto qx$ ($q\in\mathbb{C}^*$ not a root of unity), and the Mahler
operator $x\mapsto x^p$ ($p\geq 2$ integer). The only restriction is that we
constrain our solutions to be expressed as (possibly ramified) Laurent series
in the variable $x$ with complex coefficients (or in the variable $1/x$ in some
special case associated with the shift operator). Our proof is based on the
parametrized difference Galois theory initiated by Hardouin and Singer. We also
deduce from our main result a general statement about algebraic independence of
values of Mahler functions and their derivatives at algebraic points.

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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org