In this paper, we give some interesting symmetric identities of generalized higher-order Carlitz q-Bernoulli polynomials attached to χ which are derived from symmetry properties of multivariate p-adic q-integral on X.

Abstract. The goal of this paper is to construct the p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant overconvergent Shintani lifting. The classical Shintani map(see [Shn]) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. Glenn Stevens proved in [St1] that there is ...

We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use...

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...

Let p be a prime number and let K be a finite extension of Qp. Let R be the valuation ring of K, P the maximal ideal of R, and K̄ = R/P the residue field of K. Let q denote the cardinality of K̄, so K̄ ≃ Fq. For z in K, let ord z denote the valuation of z, and set |z| = q . Let f be a non constant element of K[x1, . . . , xm]. The p-adic Igusa local zeta function Z(s) associated to f (relative to ...

and Applied Analysis 3 For k ∈ N and n ∈ Z , by making use of the multivariate p-adic q-integral on Zp, we consider the following modified q-Bernoulli numbers with weight α of order k, B̃ k,α n,q :

The fundamental aim of the present paper is to deal with introducing a new family Daehee polynomials which called degenerate $q$-Daehee weight $\alpha$ by using $p$-adic $q$-integral on $\mathbb{Z}_{p}$. From this definition, we obtain some summation formulae and properties. We also introduce higher order $\alpha $ interesting identities.

and reproduction in any medium, provided the original work is properly cited. Abstract. In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Z p. By using these properties, we give some interesting identities related to higher-order q-Bernoulli polynomials.

The classical Shintani map (see [Shn]) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. In this paper, we will construct a Hecke-equivariant overconvergent Shintani lifting which interpolates the classical Shintani lifting p-adically, following the idea of G. Stevens in [St1]. In consequence, we get a formal q-expan...

In this paper, by using the p-adic q-integral on Zp which was defined by Kim, we define the weighted Carlitz q-Bernoulli polynomials and investigate some identities of these polynomials. In particular, we define the weighted degenerate Carlitz’s q-Bernoulli polynomials and numbers and give some interesting properties that are associated with these numbers and polynomials. AMS subject classifica...