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An approach to define the resultant of two entire functions. (English) Zbl 1369.30005
Let \(f_n(z)=a_0+a_1z+\dots+ a_nz^n\), \(a_n\neq 0\), \(g_m(z)=b_0+b_1z+\dots+ b_mz^m\), be polynomials. The classical resultant \(R(f_n, g_m)\) of \(f_n\) and \(g_m\) can be written in the form \(R(f_n, g_m)=a_n^m \prod_{k=1}^{n} g_m(\alpha_k)\) where \(\alpha_1, \dots, \alpha_n\) are zeros of \(f_n\). Using this property the authors introduce the resultant of two entire functions, where one of them has finitely many zeros. Some formulas for the calculation of the resultant in terms of determinants are established.

MSC:
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
30D10 Representations of entire functions of one complex variable by series and integrals
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