Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the sharpness of a three circles theorem for discrete harmonic
  functions   Any three circles theorem for discrete harmonic functions must contain an
inherent error term. In this paper we find the sharp error term in an
$L^2$-three circles theorem for harmonic functions defined in $\Zb^2$. The
proof is highly indirect due to combinatorial obstacles and cancellations
phenomena. We exploit Newton interpolation methods and recursive arguments.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph