Related papers: New p-adic hypergeometric functions and syntomic r…
We introduce a new family of special functions, namely $q$-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to $q$-analogues of Poisson distributions. We focus our attention on their structural…
We illustrate the theory of the radius of convergence of a connection on a p-adic curve X, by deducing from it a simple proof of a variant of Alain Robert's p-adic Rolle theorem. We need to carefully compare our global notion of radius of…
The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.
We use the Dwork-Frobenius operator to prove an integrality result for $A$-hypergeometric series whose coefficients are factorial ratios. As a special case, we generalize one direction of a classical result of Landau on the integrality of…
We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…
Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of $p$-adic $L$-functions (of Bella\"iche and Stevens) over the eigencurve. As the first ingredient, we…
This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the…
We introduce a new collection of special functions associated to a complex curve of genus 2 similar to Kleinian hyperelliptic $\sigma$-function. These functions are related to weight 2 $\theta$-functions in the same fashion as…
Wiles' work on Fermat's last Theorem highlighted the power of $p$-adic methods to prove the existence of analytic continuations of $\zeta$ and $L$ functions. These methods have become considerably more sophisticated in recent years, and…
In this paper, two new classes of convex functions as a generalization of convexity which is called (h-s)_{1,2}-convex functions are given. We also prove some Hadamard-type inequalities and applications to the special means are given.
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the…
We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…
We construct $p$-adic multiple $L$-functions in several variables, which are generalizations of the classical Kubota-Leopoldt $p$-adic $L$-functions, by using a specific $p$-adic measure. Our construction is from the $p$-adic analytic side…
We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gau\ss's ${}_2 F_{1}$, Thomae's ${}_L F_{L-1}$ and Appell-Lauricella's $F_D$. In particular, we present a fundamental system of…
We give a criterion of integrality of an one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a p-adic analytic formula for the…
We produce a decomposition of the parameter space of the $A$-hypergeometric system associated to a projective monomial curve as a union of an arrangement of lines and its complement, in such a way that the analytic behavior of the solutions…
Since Rob Pollack and Glenn Stevens used overconvergent modular symbols to construct p-adic L-functions for non-critical slope rational modular forms, the theory has been extended to construct p-adic L-functions for non-critical slope…
We define new objects called 'horizontal $p$-adic $L$-functions' associated to $L$-values of twists of elliptic curves over $\mathbb{Q}$ by characters of $p$-power order and conductor prime to $p$. We study the fundamental properties of…
It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use…
We study the convexity properties of the generalized trigonometric functions considered as functions of parameter. We show that $p\to\sin_p(y)$ and $p\to\cos_p(y)$ are log-concave on the appropriate intervals while $p\to\tan_p(y)$ is…