Equivalence between the methods involving Fourier series and Poisson's summation formula, and the evaluation of a class of lattice sums in arbitrary dimensions

The authors bring out the similarities between the Fourier series method and Poisson's summation formula method by evaluating the lattice sum g(r) identical to Σ/sub tau/e/sup -λ absolute value of r-tau// absolute value of r-tau over a Bravais lattice {tau} in three dimensions, λ and r being independent of tau. The authors show that the two approaches are actually equivalent by proving that Poisson's summation formula (in any dimensionality) can, itself, be derived from the Fourier-series method. Also they present an expression, suitable for quick use, for a class of lattice sums Σ/sub tau/F(absolute value of r-tau) over a Bravais lattice {tau} in arbitrary dimensions