APPROXIMATE SEVERAL ZEROS OF A CLASS OF PERIODICAL COMPLEX FUNCTIONS

This paper discussed the number of zeroes of the complex function F : C --> C defined by [GRAPHICS] where Im(Z) is the imaginary part of Z, \a(n)\ + \b(n)\ not-equal 0. Let n1 = max\1 less-than-or-equal-to k less-than-or-equal-to n {0,k\b(k) not-equal -ia(k)} and n2 = max\1 less-than-or-equal-to k less-than-or-equal-to n {0,k\b(k) not-equal ia(k)}. We prove that if 0 is a regular value of F and n1n2 not-equal 0, then F has at least n1 + n2 zeroes in domain (0,2-pi] x R and n1 + n2 of them can be located with the homotopy method simultaneously. Furtheromore, if alpha-1 = ... = alpha(m) = 0 and n1n2 not-equal 0, then F has exactly n1 + n2 zeroes in domain (0, 2-pi] x R.