V. Shemyakov

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20232026

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math.CV2023

The zeta function of zeros and poles of a meromorphic function, the criterion for the absence of zeros, and its application to sums of Cauchy kernels

Vladimir Shemyakov

A connection between the zeta functions of zeros and poles of a meromorphic function has been established, and using it, a criterion for the absence of zeros has been derived. Suff…

math.CV2023

Zeros of meromorphic functions of the form $n \sum \frac{c _{n}}{( z - t _{n} ) ^{2}}$

Anton Baranov, Vladimir Shemyakov

We study zeros distribution for meromorphic functions of the form $n \sum \frac{c _{n}}{( z - t _{n} ) ^{2}}$ , where $n \sum \frac{∣ c _{n} ∣}{∣ t _{n} ∣ ^{2}} < \infty$ . We prove an analog o…

The zeta function of zeros and poles of a meromorphic function, the criterion for the absence of zeros, and its application to sums of Cauchy kernels

Zeros of meromorphic functions of the form n∑​(z−tn​)2cn​​

Zeros of meromorphic functions of the form $n \sum \frac{c _{n}}{( z - t _{n} ) ^{2}}$