  Structures of the disconnected part of higher genus superstring amplitudes
restricted to the hyper elliptic cases are investigated in the NSR formalism,
based on the DHoker Phong and recent results. A set of equations, which we can
regard as a basic tool to sum over the spin structures of any of g loop, M
point amplitudes systematically, is shown by using a classical result of
Abelian functions. We discuss structures of g loop, M point massless external
boson superstring amplitudes by assuming that the spin structure dependence of
any of the disconnected amplitudes is only on one kind of constants, the genus
g Weierstrass Pe function valued at the summation of g number of half periods
chosen out of 2g+1 half periods. This is a natural generalization of the case
of genus 1. This assumption will be validated by a conjectured theorem which
states that the spin structure dependent part of any string amplitude will be
naturally decomposed into two parts. One is composed of manifestly modular
invariant functions of positions of inserting operators, and the other is the
polynomial of Pe function constants related to the moduli of Riemann surfaces
only. It is shown that this is actually the case for any M for g=1, and M=1,2,3
for any g. Due to a technical problem, our consideration is at present
restricted to the case that g(g+1)divided by 2 is odd. Example calculations are
shown for the genus 2 by the method described here. In particular, our method
correctly reproduces biholomorphic 1 form of DHoker Phong result as for the
four point amplitudes of the disconnected parts.
