ABSTRACT
First we deal with lattice functions corresponding to higher order differential operators. We present some preparatory material on the Riemann zeta function in its relationship to lattice functions (for early references see, e.g., L.J. Mordell [1928a, b, 1929]). It should be mentioned that the one-dimensional Riemann zeta function is introduced here in such a way that its extension to the multivariate case becomes apparent. The trapezoidal rule is seen in its relationship to Euler and Poisson summation formulas. The classical Romberg integration rule is recapitulated. Finally, remainder terms for the trapezoidal rule are estimated in terms of special values of the Riemann zeta function.
