Related papers: General coefficient-vanishing results associated w…
We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…
Based on a classical result on partitions of an integer into a finite set of positive integers, we establish a general positivity result on coefficients of certain $q$-series which uniformly refines the positivity of truncated pentagonal…
Motivated by an analysis of causal mechanism from economic stress to entrepreneurial withdrawals through depressed affect, we develop a two-layer generalized varying coefficient mediation model. This model captures the bridging effects of…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
In fully-implicit two-phase pore-network models, developing a well-converged scheme remains a major challenge, primarily due to the discontinuities in the phase conductivities. This paper addresses these numerical issues by proposing a…
A new meta-algorithm for estimating the conditional average treatment effects is proposed in the paper. The main idea underlying the algorithm is to consider a new dataset consisting of feature vectors produced by means of concatenation of…
Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of projective modules over noncommutative tori (theta-vectors).…
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…
This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…
In this paper we deal with the generalized Gamma processes and their compositions. For the compositions of two or more than two generalized Gamma processes we give, when possible, the explicit law whereas, in the other cases the…
We establish discrete and continuous log-concavity results for a biparametric extension of the $q$-numbers and of the $q$-binomial coefficients. By using classical results for the Jacobi theta function we are able to lift some of our…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
We study concave trace functions of several operator variables and formulate and prove multivariate generalisations of the Golden-Thompson inequality. The obtained results imply that certain functionals in quantum statistical mechanics have…
Quite recently, the first author investigated vanishing coefficients of the arithmetic progressions in several $q$-series expansions. In this paper, we further study the signs of coefficients in two $q$-series expansions and establish some…
The paper develops the result of second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest non-vanishing derivatives of theta functions with singular…
We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…