V. Shemyakov

collaborators

4 papers

math.CV2026

Second-Order Differential Equations and Sums of Squares of Cauchy Kernels with Finitely Many Zeros

Vladimir Shemyakov

We study finite-order meromorphic functions representable as absolutely convergent sums of squares of Cauchy kernels and having only finitely many zeros. By earlier work of Baranov…

math.CV2024

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…

math.CV2024

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.CV2024

The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity

Vladimir Shemyakov

In analysis, it's often useful to know the value of a function at infinity, this operation possesses pleasant properties. However, even when the limit does not exist, some intuitiv…

Second-Order Differential Equations and Sums of Squares of Cauchy Kernels with Finitely Many Zeros

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

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

The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity

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