Tests for polynomial zeros on a polydisc distinguished boundary

That several applications require the testing for zeros on the distinguished boundary of an unit polydisc of a multivariable polynomial has been noted. Here, procedures to. test whether or not a polynomial
B(z_1 , z_2,\cdots,z_n)
has zeros on
|z_1| = |z_2| = \cdots = |z_n|= 1
are developed. Two indirect tests are fornulated and the details of a direct test are given for the
n = 2
case with possible extensions for the
n
> 2 case noted. Singular cases are given adequate attention.