Epstein Zeta Function

$$Z\left\vert\matrix{{\bf g}\cr {\bf h}\cr}\right\vert (q;s)=\... ...-2\pi i{\bf h}\cdot{\bf l}}\over [q({\bf l}+{\bf g})]^{s/2}},$$

where ${\bf g}$ and ${\bf h}$ are arbitrary Vectors, the Sum runs over a $d$-dimensional Lattice, and ${\bf l}= -{\bf g}$ is omitted if ${\bf g}$ is a lattice Vector.

See also Zeta Function

References

Glasser, M. L. and Zucker, I. J. ``Lattice Sums in Theoretical Chemistry.'' Theoretical Chemistry: Advances and Perspectives, Vol. 5. New York: Academic Press, pp. 69-70, 1980.

Shanks, D. ``Calculation and Applications of Epstein Zeta Functions.'' Math. Comput. 29, 271-287, 1975.