Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A lemma on the difference quotients   Using a new Borel type growth lemma, we extend the difference analogue of the
lemma on the logarithmic derivative due to Halburd and Korhonen to the case of
meromorphic functions $f(z)$ such that $\log T(r,f)\leq r/(\log r)^{2+\nu}$,
$\nu>0$, for all sufficiently large $r$. The method by Halburd and Korhonen
implies an estimate for the lemma on difference quotients, where the
exceptional set is of finite logarithmic measure. We show the necessity of this
set by proving that it must be of infinite linear measure for meromorphic
functions whose deficiency is dependent on the choice of the origin. In
addition, we show that there is an infinite sequence of $r$ in the set for
which $m(r,f(z+c)/f(z))$ is not small compared to $T(r,f)$ for entire functions
constructed by Miles. We also give a discrete version of Borel type growth
lemma and use it to extend Halburd's result on first order discrete equations
of Malmuist type.

29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat