Related papers: p-adic l-functions and sums of powers

This paper gives new explicit formulas for sums of powers of integers and their reciprocals.

The goal of this article is twofold. We first extend a result of Murty and Saradha \cite{MS} related to the digamma function at rational arguments. Further, we extend another result of the same authors \cite{MS1} about the nature of…

In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between…

This paper looks at the L-function of the k-th symmetric power of the ell-adic sheaf over the affine line associated to the generalized Airy family of exponential sums. We compute the degree of this rational function and the local factors…

In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.

The purpose of this paper is to construct the p-adic twisted (h,q)-Euler-l-function, which interpolates the twisted generalized twisted Euler numbers attached to chi at a negative integer.

In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.

The definition for the $p$-adic Hurwitz-type Euler zeta functions has been given by using the fermionic $p$-adic integral on $\mathbb Z_p$. By computing the values of this kind of $p$-adic zeta function at negative integers, we show that it…

This paper evaluates some generalised Euler sums involving the digamma function.

The aim of this paper is to derive on the basis of the Euler's formula several analytical relations which hold for certain classes of planar graphs and which can be useful in algorithmic graph theory.

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…

The purpose of this paper is to construct p-adic Dedekind sums and Hardy-Berndt type sums. We also construct generating function of the twisted Bernoulli polynomials and functions. Furthermore, we give some discussions on elliptic analogue…

In this paper, we compute the $q$-adic slopes of the L-functions of an important class of exponential sums arising from analytic number theory. Our main tools include Adolphson-Sperber's work on toric exponential sums and Wan's…

We present an efficient algorithm for computing certain special values of Rankin triple product $p$-adic L-functions and give an application of this to the explicit construction of rational points on elliptic curves.

In this paper, we will study p-adic q-expansion of alternating sums of powers. From these properties, we derive some interesting properties related to p-adic q-expansion of alternating sums of powers

In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…

The purpose of this article is to newly define the $p$-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special…

One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler…

In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.

In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator. Also, we show between the q-Euler…