TY - JOUR
T1 - On the Number of Zeroes of Exponential Systems
AU - Gao , Tang-An
AU - Wang , Ze-Ke
JO - Journal of Computational Mathematics
VL - 3
SP - 256
EP - 261
PY - 1991
DA - 1991/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9399.html
KW - 
AB - <p style="text-align: justify;">A system $E:C^n\rightarrow C^n$ is said to be an exponential one if its terms are $ae^{im_1Z_1}.\cdots .e^{im_nZ_n}$. This paper proves that for almost every exponential system $E:C^n\rightarrow C^n$ with degree $(q_1,\cdots,q_n)$, $E$ has exactly $\Pi^n_j=1(2q_j)$ zeroes in the domain $D=\{(Z_1,\cdots,Z_n)\in C^n:Z_j=x_j+iy_j,x_j,y_j\in R,0\leq x_j&lt;2\pi ,j=1,\cdots,n\}$, and all these zeroes can be located with the homotopy method.</p>