相关论文: On special values of generalized $p$-adic hypergeo…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…

We relate the $p$-adic heights of generalized Heegner cycles to the derivative of a $p$-adic $L$-function attached to a pair $(f, \chi)$, where $f$ is an ordinary weight $2r$ newform and $\chi$ is an unramified imaginary quadratic Hecke…

In this paper we achieve some new Hadamard type inequalities using elementary well known inequalities for functions whose first derivatives absolute values are s-geometrically and geometrically convex. And also we get some applications for…

The definition of a holomorphic function over a general measurable space $S$ endowed with a Markov process is defined by Zeghib and Barre. In this article we consider holomorphic functions over graphs whose ranges are a given finite field…

We give a definition of generalized hypergeometric functions over finite fields using modified Gauss sums, which enables us to find clear analogy with classical hypergeometric functions over the complex numbers. We study their fundamental…

In this paper, we introduce degenertae generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involving of lambda-binomial coefficients and lambda-falling sequence, and can be represented…

We generalize some of the results of Andreatta, Iovita, and Pilloni and the author to Hodge type Shimura varieties having non-empty ordinary locus. For any $p$-adic weight $\kappa$, we give a geometric definition of the space of…

In the previous paper by Asakura-Otsubo-Terasoma, we prove that the special values of the hypergeometric function 3F2 at 1 are linear combinations of logarithms of algebraic numbers and 1 over algebraic numbers, if exponents are rational…

Recently, there emerges different versions of beta function and hypergeometric functions containing extra parameters. Gaining enlightenment from these ideas, we will first introduce a new extension of generalized hypergeometric function and…

We derive properties of $\pi(x)$ reminiscent of those of the logarithm and absolute value functions. Two of these properties are similar to the relations defining the linearity of a function. Several applications of these properties of…

Let ${\mathbb Z}_p$ denote the ring of all $p$-adic integers and call $${\mathcal U}=\{(x_1,\ldots,x_n):\,a_1x_1+\ldots+a_nx_n+b=0\}$$ a hyperplane over ${\mathbb Z}_p^n$, where at least one of $a_1,\ldots,a_n$ is not divisible by $p$. We…

This article presents an approach to the algebraic functional equation for Selmer complexes, which in turn have applications in the Iwasawa theoretic study of Rankin-Selberg products of the Hida and Coleman families. Our treatment…

In this paper, we confirm several conjectures posed by Sun recently; for example, we prove that for any odd prime $p$ we have $$ \sum_{k=0}^{p-1}A_k\equiv\begin{cases}4x^2-2p\pmod{p^2}\quad&\text{if $p=x^2+2y^2\ (x,y\in\mathbb{Z})$},\\…

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…

The main aim of the present work is to give some interesting the $q$-analogues of various $q$-recurrence relations, $q$-recursion formulas, $q$-partial derivative relations, $q$-integral representations, transformation and summation…

In \cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\cdots]$ using the Teichm\"{u}ller character of finite fields and quotients of the $p$-adic gamma function. This function extends hypergeometric functions over finite fields to the…

The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this…

In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…

Classification of AS-regular algebras is one of the most important projects in noncommutative algebraic geometry. Recently, Itaba and the first author gave a complete list of defining relations of $3$-dimensional quadratic AS-regular…