相关论文: Estimates of the logarithmic derivative near a sin…
We derive approximate formulas for the logarithmic de- rivative of the Selberg and Ruelle zeta functions over compact, even- dimensional, locally symmetric spaces of rank one. The obtained for- mulas are given in terms of the…
For $f$ analytic and close to convex in $D=\{z: |z|< 1\}$, we give sharp estimates for the logarithmic coefficients $\gamma_{n}$ of $f$ defined by $\log \dfrac{f(z)}{z}=2\sum_{n=1}^{\infty} \gamma_{n}z^{n}$ when $n=1, 2,3$.
We obtain an estimate for uniform approximation rate of bounded analytic in the unit disk functions by logarithmic derivatives of $C$-polynomials, i.e., polynomials, all of whose zeros lie on the unit circle $C:|z|=1$.
The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is…
We investigate the distribution of the logarithmic derivative of the Riemann zeta-function on the line Re(s)=\sigma, where \sigma, lies in a certain range near the critical line \sigma=1/2. For such \sigma, we show that the distribution of…
It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function $f(z)$, \begin{equation*} m\left(r,\frac{\Delta_cf - ac}{f' - a}\right)=S(r,f'), \end{equation*} where $\Delta_c f=f(z+c)-f(z)$ and…
For a linear differential equation with a mild condition on its singularities, we discuss generalized continued fractions converging to expressions in its solutions and their derivatives. In the case of an order two linear differential…
The first objective of the paper is to estimate logarithmic partial derivative for meromorphic functions in several complex variables. Our estimations for logarithmic partial derivatives extend the results of Gundersen \cite{GG2} to the…
The logarithmic coefficients $\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty}…
For univalent and normalized functions $f$ the logarithmic coefficients $\gamma_n(f)$ are determined by the formula $\log(f(z)/z)=\sum_{n=1}^{\infty}2\gamma_n(f)z^n$. In the paper \cite{Pon} the authors posed the conjecture that a locally…
In this article, we study the growth of solutions of the homogeneous complex linear differential equation \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{\prime}+ A_{0}(z)f=0, \end{equation*}% where the coefficients…
The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…
In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.
The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…
The logarithmic coefficients $\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$ is defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty}…
We study the distributions of values of the logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main object is determining and investigating the density functions of such value-distributions for any…
This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the…
For an analytic and univalent function $f$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$, the logarithmic coefficients $\gamma_n$ are defined by $\log \frac{f(z)}{z}= 2\sum_{n=1}^{\infty}…
Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L'/L\right)\left(\sigma,\chi\right)$ of Dirichlet $L$-functions, where $\chi$ is a primitive character modulo…
In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…