Related papers: Linear independence of Gamma values in positive ch…

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to…

We present a new method for algebraic independence results in the context of Mahler's method. In particular, our method uses the asymptotic behaviour of a Mahler function $f(z)$ as $z$ goes radially to a root of unity to deduce algebraic…

We provide a new, elementary proof of the multiplicative independence of pairwise distinct $\mathrm{GL}_2^+(\mathbb{Q})$-translates of the modular $j$-function, a result due originally to Pila and Tsimerman. We are thereby able to…

In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…

We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions…

This paper studies rational functions $\mathfrak{J}_\alpha(q)$, which depend on a positive element $\alpha$ of the root lattice of a root system. These functions arise as Shapovalov pairings of Whittaker vectors in Verma modules of highest…

We prove new linear independence results for the values of generalized hypergeometric functions ${}_pF_q$ at several distinct algebraic points, over arbitrary algebraic number fields. Our approach combines constructions of type II Pad\'{e}…

We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of…

We study the values taken by Gamma_0(n) modular functions at elliptic points of order 2 for the Fricke extension that lie outside Gamma_0(n). In the case of a principal modulus (`Hauptmodul') for Gamma_0(n) or its Fricke extension, we…

This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for…

We revisit the computation of the beta function in the two-dimensional $\mathbb{CP}(1)$ sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum-independent tadpoles or even…

In this paper, we give a precise definition of an analytic $\gamma$-factor of an irreducible representation of a classical group over a local function field of odd characteristic so that it satisfies some notable properties which are enough…

In this paper, we study the algebraic relations satisfied by the solutions of $q$-difference equations and their transforms with respect to an auxiliary operator. Our main tool is the parametrized Galois theories developed in two papers.…

Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…

We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

This paper investigates the lemniscate starlikeness of analytic functions by deriving specific conditions on their power series coefficients. The study utilizes the Cauchy product of power series along with key inequalities involving the…

In this article, we present a new linear independence criterion for values of the $p$-adic polygamma functions defined by J.~Diamond. As an application, we obtain the linear independence of some families of values of the $p$-adic Hurwitz…

In this paper, by using the residue theorem and asymptotic formulas of trigonometric and hyperbolic functions at the poles, we establish many relations involving two or more infinite series of trigonometric and hyperbolic trigonometric…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…