Related papers: Hankel-type determinants and Drinfeld quasi-modula…
We study certain correspondences over Drinfeld modular varieties given by sums of Hecke correspondences. We propose generalizations of Stickelberger's theorem for higher dimensions. Using this result, we study anihilators for some cusp…
We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the…
The aim of this paper is to describe some partial advances in the solution of the following two problems. Find the maximal order of vanishing at infinity of a non-zero Drinfeld quasi-modular form of given weight. Determine differential…
The middle binomial coefficients can be interpreted as numbers of Motzkin paths which have no horizontal steps at positive heights. Assigning suitable weights gives some nice polynomial extensions. We determine the Hankel determinants and…
Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials $B_{2k+1}(x)$ and the Euler polynomials $E_{2k+\nu}(x)$, for $\nu=0, 1,…
Let $f$ be analytic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order $\alpha$,…
This paper contains the written notes of a course the author gave at the VIASM of Hanoi in the Summer 2018. It provides an elementary introduction to the analytic naive theory of Drinfeld modular forms for the simplest 'Drinfeld modular…
In this paper we give the upper bounds of the Hankel determinants of the second and third order for the class $\mathcal{S}$ of univalent functions in the unit disc.
We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with…
Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical…
Using some properties of the Grunsky coefficients we improve earlier results for upper bounds of the Hankel determinants of the second and third order for the class $\mathcal{S}$ of univalent functions.
In this paper we give improved, probably not sharp, upper bounds of the Hankel determinant of third order for various classes of univalent functions and conjecture the sharp one.
We define the notion of factorizable quasi-Hopf algebra by using a categorical point of view. We show that the Drinfeld double $D(H)$ of any finite dimensional quasi-Hopf algebra $H$ is factorizable, and we characterize $D(H)$ when $H$…
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…
We derive a general expression for the Hankel determinants of a Dirichlet series F(s) and derive the asymptotic behavior for the special case that F(s) is the Riemann zeta function. In this case the Hankel determinant is a discrete analogue…
In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are…
In the present study, we consider two subclasses starlike and convex functions, denoted by $\mathcal{S}_{\mathcal{B}}^{*}$ and $\mathcal{C}_{\mathcal{B}}$ respectively, associated with a bean-shaped domain. Further, we estimate certain…
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials.
Let $F$ be a function field over $\mathbb{F}_q$, $A$ its ring of regular functions outside a place $\infty$ and $\mathfrak{p}$ a prime ideal of $A$. First, we develop Hida theory for Drinfeld modular forms of rank $r$ which are of slope…
In this paper we determine the upper bounds of $|H_{2}(3)|$ for the inverse functions of functions of some classes of univalent functions, where $H_{2}(3)(f)=a_{3}a_{5}-a_{4}^{2}$ is the Hankel determinant of a special type.