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DOI: 10.23671/VNC.2017.1.5820 On Distribution of Zeros for a Class of Meromorphic Functions
Korobeinik Yu. F.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 1.
Abstract:
In this article some class \(\mathcal{K}_0\) of meromorphic functions is introduced. Each function \(y(z)\) from \(\mathcal{K}_0\) satisfies the functional equation \(y(z)=b_y(z)y(1z)\) with its own "Riemann's multiplier" \(b_y(z)\) which is a meromorphic function with real zeros and poles. All poles of an arbitrary function from \(\mathcal{K}_0\) are real and belong to the interval \((\frac12,\frac12+h_1]\), \(h_1=h_1(y)\). Using the theory of residues we prove some relation connecting the following mag\ni\tu\des: \(\mathcal{P}_y\), the sum of all orders of poles of \(y \in \mathcal{K}_0\); \(\mathcal{N}_y(T)\), the sum of multiplicities of all zeros of \(y\) having the form \(\frac12 +i\tau\), \(\tau
Keywords: zeros of meromorphic functions, functional equation.
Language: Russian
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For citation: Korobeinik Yu. F. On Distribution of Zeros for a Class of Meromorphic Functions. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 4149. DOI 10.23671/VNC.2017.1.5820 ← Contents of issue 
 

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