Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On generalized Eisenstein series and Ramanujan's formula for periodic
  zeta-functions   In this paper, transformation formulas for a large class of Eisenstein series
defined by \[
G(z,s;A_{\alpha},B_{\beta};r_{1},r_{2})=\sum\limits_{m,n=-\infty}^{\infty }\
\hspace{-0.19in}^{^{\prime}}\frac{f(\alpha m)f^{\ast}(\beta n)}
{((m+r_{1})z+n+r_{2})^{s}},\text{ }\operatorname{Re}(s)>2,\text{
}\operatorname{Im}(z)>0 \] are investigated for $s=1-r$, $r\in\mathbb{N}$. Here
$\left\{ f(n)\right\}$ and $\left\{ f^{\ast}(n)\right\}$, $-\infty<n<\infty$
are sequences of complex numbers with period $k>0$, and $A_{\alpha}=\left\{
f(\alpha n)\right\} $ and $B_{\beta}=\left\{ f^{\ast}(\beta n)\right\}$,
$\alpha,\beta\in\mathbb{Z}$. Appearing in the transformation formulas are
generalizations of Dedekind sums involving the periodic Bernoulli function.
Reciprocity law is proved for periodic Apostol-Dedekind sum outside of the
context of the transformation formulas. Furthermore, transformation formulas
are presented for $G(z,s;A_{\alpha},I;r_{1},r_{2})$ and $G(z,s;I,A_{\alpha
};r_{1},r_{2})$, where $I=\left\{ 1\right\}$. As an application of these
formulas, analogues of Ramanujan's formula for periodic zeta-functions are
derived.

35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an