Title: Counting Multiplicities in a Hypersurface over a Number Field,
Abstract: We fix a counting function of multiplicities of algebraic points in a
projective hypersurface over a number field, and take the sum over all
algebraic points of bounded height and fixed degree. An upper bound for the sum
with respect to this counting function will be given in terms of the degree of
the hypersurface, the dimension of the singular locus, the upper bounds of
height, and the degree of the field of definition.