相关论文: Sato-Tate Distribution of $p$-adic hypergeometric …
Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…
Hecke operators acting on modular functions arise naturally in the context of 2d conformal field theory, but in seemingly disparate areas, including permutation orbifold theories, ensembles of code CFTs, and more recently in the context of…
Let $k=\mathbb{Q}(\sqrt{-3})$, and let $c\in \mathfrak{O}_k$ be a square free algebraic integer such that $c\equiv 1~({\rm mod}~{\langle9\rangle})$. Let $\zeta_{k(c^{1/3})}(s)$ be the Dedekind zeta function of the cubic field $k(c^{1/3})$…
We show that the action of Hecke operators away from $p$ on the space of ($p$-adic) overconvergent modular forms is ($p$-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended…
We define the adelic hypergeometric function of special Gaussian type by means of a tower of hypergeometric curves. This function takes values in an adelic completed group ring and interpolates all the hypergeometric functions of the same…
We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kahler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
In his work studying the Zeta functions of families of hypersurfaces, Dwork came upon a one-parameter family of hypersurfaces (now known as \emph{the} Dwork family). These examples were not only useful to Dwork in his study of his…
Motivated by multi-topology building and city model data, first a lossless representation of multiple $T_0$-topologies on a given finite set by a vertex-edge-weighted graph is given, and the subdominant ultrametric of the associated…
We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (GSE) ensembles, using semi-classical skew-orthogonal…
In a recent paper (Asci \textit{et al.}, 2008) it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function $_{2}F_{1}$. In the present paper we fully exploit a…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
For primes p congruent to 1 mod 12, we present an explicit relation between the traces of Frobenius on a family of elliptic curves with j-invariant 1728/t and values of a particular 2F1-hypergeometric function over F_p. Additionally, we…
In this note, we define and study Asai gamma factors over finite fields. We also prove some results about local Asai L-functions over p-adic fields for level zero representations.
In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural…
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the…
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite…
We consider Gibbs distributions, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval…
We establish the two-dimensional asymptotic distributions of the logarithm and logarithmic derivative of $L$-functions associated with a family of cubic Hecke characters. A crucial ingredient in the proof of our main result is an…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…