Related papers: The third logarithmic coefficient for the class S

In this paper we consider a simple linear recurrence sequence $ G_n $ defined over a function field in one variable over the field of complex numbers. We prove an upper bound on the indices $ n $ and $ m $ such that $ G_n + G_m $ is an $ S…

We give a refined upper bound for the hyperbolic volume of an alternating link in terms of the first three and the last three coefficients of its colored Jones polynomial.

We show an alternative proof of the sharpest known lower bound for the logarithmic energy on the unit sphere $\mathbb{S}^2$. We then generalize this proof to get new lower bounds for the Green energy on the unit $n$-sphere $\mathbb{S}^n$.

We study noncommutative versions of holomorphic and harmonic functions on the unit disk.

An algorithm for computing the limit of a quotient of bivariate real analytic functions has been developed by one of the authors in (Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, 50, 2013, 197…

In the present paper, a subclass of analytic and bi-univalent functions by means of (p; q)- Lucas polynomials is introduced. Certain coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szego…

In this paper a survey is given of application of a method based on Grunsky coefficients for obtaining different estimates (some sharp) for the general class of univalent functions where no analytical characterisation exists. More…

In this paper we prove a recent conjecture formulated by Dmitrishin, Smorodin and Stokolos about that certain polynomials are univalent in the unit disk. As a consequence we get an upper estimate for the Koebe radius of univalent…

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…

In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$\alpha$-analytic functions. First, by using a new idea, we prove an improved lemma and the coefficient estimates for bounded polyanalytic…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded $S$-modules $\Tor_i^S(M,I^k)$ and $\Ext^i_S(M,I^k)$ are…

Let ${\mathcal U}(\lambda)$ denote the family of analytic functions $f(z)$, $f(0)=0=f'(0)-1$, in the unit disk $\ID$, which satisfy the condition $\big |\big (z/f(z)\big )^{2}f'(z)-1\big |<\lambda $ for some $0<\lambda \leq 1$. The…

Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these…

In this paper we provide a computation of the mod 2 cohomology groups of the third finite subset space of the sphere $S^n$ using known results about the cohomology of the symmetric product of spheres.

We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic…

We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound for another version of the slice genus proposed here: the…

We prove a new upper bound for the number of smooth values of a polynomial with integer coefficients. This improves Timofeev's previous result unless the polynomial is a product of linear polynomials with integer coefficients. As an…

Let X be a smooth variety over a field of positive characteristic, and let E be an overconvergent isocrystal on X. We establish a criterion for the existence of a "canonical logarithmic extension" of E to a good compactification of X. In…

We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…

In the present paper, we were mainly concerned with obtaining estimates for the general Taylor-Maclaurin coefficients for functions in a certain general subclass of analytic bi-univalent functions. For this purpose, we used the Faber…