Bulletin of the
Korean Mathematical Society BKMS

In this paper, for $a\in \mathbb{C}$, we investigate functions $g_{a}$ and $ \psi _{a}$ associated with three term relations. $g_{a}$ is defined by means of function $\psi _{a}$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_{a}$.

Keywords: three term relations, period function, Eisenstein series, Riemann zeta function

MSC numbers: Primary 30D05, 39A10; Secondary 11M32, 11M36