Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the theorem of Davenport and generalized Dedekind sums   A symmetrized lattice of $2n$ points in terms of an irrational real number
$\alpha$ is considered in the unit square, as in the theorem of Davenport. If
$\alpha$ is a quadratic irrational, the square of the $L^2$ discrepancy is
found to be $c( \alpha ) \log n + O \left( \log \log n \right)$ for a
computable positive constant $c( \alpha )$. For the golden ratio $\varphi$, the
value $\sqrt{c (\varphi ) \log n}$ yields the smallest $L^2$ discrepancy of any
sequence of explicitly constructed finite point sets in the unit square. If the
partial quotients $a_k$ of $\alpha$ grow at most polynomially fast, the $L^2$
discrepancy is found in terms of $a_k$ up to an explicitly bounded error term.
It is also shown that certain generalized Dedekind sums can be approximated
using the same methods. For a special generalized Dedekind sum with arguments
$a, b$ an asymptotic formula in terms of the partial quotients of $\frac{a}{b}$
is proved.

19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas