Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a generalization of Menon-Sury identity to number fields involving a
  Dirichlet Character   For every positive integer $n$, Sita Ramaiah's identity states that \medskip
\begin{equation*} \sum_{a_1, a_2, a_1+a_2 \in (\mathbb{Z}/n\mathbb{Z})^*}
\gcd(a_1+a_2-1,n) = \phi_2(n)\sigma_0(n) \; \text{ where } \; \phi_2(n)=
\sum_{a_1, a_2, a_1+a_2 \in (\mathbb{Z}/n\mathbb{Z})^*} 1, \end{equation*}
\medskip where $(\mathbb{Z}/n\mathbb{Z})^*$ is the multiplicative group of
units of the ring $\mathbb{Z}/n\mathbb{Z}$ and $\sigma_s(n) =
\displaystyle\sum_{d\mid n}d^s$.
  \smallskip
  This identity can also be viewed as a generalization of Menon's identity. In
this article, we generalize this identity to an algebraic number field $K$
involving a Dirichlet character $\chi$. Our result is a further generalization
of a recent result in \cite{wj} and \cite{sury}.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con