  We analyse the number of occurrences of a fixed non-zero digit in the width-w
non-adjacent forms of all elements of a lattice in some region (e.g. a ball).
Our result is an asymptotic formula, where its main term coincides with the
full block length analysis. In its second order term a periodic fluctuation is
exhibited. The proof follows Delange's method. This result in a general lattice
set-up is then used for numeral systems with an algebraic integer as base.
Those come from efficient scalar multiplication methods (Frobenius-and-add
methods) in hyperelliptic curves cryptography, and our result is needed for
analysing the running time of such algorithms.
