The Genocchi numbers and polynomials possess many interesting properties and are arising in many areas of mathematics and physics. Recently, many mathematicians have studied in the area of the q-Genocchi numbers and polynomials see 1–13 . In this paper, we construct a new type of q-Genocchi numbers G α,β n,q and polynomials G α,β n,q x with weight α and weak weight β. Throughout this paper, we ...

The purpose of the present paper is to show that morphisms between the generic fibers of truncated Barsotti-Tate group schemes over mixed characteristic complete discrete valuation rings with perfect residue fields extend in a “tame-blind” fashion — i.e., under a condition which is unaffected by passing to a tame extension — to morphisms between the original truncated Barsotti-Tate group scheme...

We show how tropical varieties of ideals I E K[x] over a field K with non-trivial valuation can always be traced back to tropical varieties of ideals π−1I E RJtK[x] over some dense subring R in its ring of integers. Moreover, for homogeneous ideals, we present algorithms on how the latter can be computed in finite time, provided that π−1I is generated by elements in R[t, x]. While doing so, we ...

In this article we prove a Grothendieck trace formula for L-functions of not necessarily commutative adic sheaves.

Using computer, a realistic study for new analogs of weighted q-Euler numbers and polynomials is very interesting. It is the aim of this paper to observe an interesting phenomenon of ‘scattering’ of the zeros of the weighted q-Euler polynomials E (α) n,q (x). The outline of this paper is as follows. In Section 2, we study weighted q-Euler polynomials E (α) n,q (x). In Section 3, we describe the...

In the recent, many mathematicians studied the multiple zeta function in the complex number field. In this paper we construct the p-adic analogue of multiple zeta function which interpolates the generalized multiple Bernoulli numbers attached to χ at negative integers. §1. Introduction Let p be a fixed prime. Throughout this paper Z p , Q p , C and C p will, respectively, denote the ring of p-a...

In this article, we consider the estimation of exponential sums along the points of the reduction mod pm of a p-adic analytic submanifold of Zp . More precisely, we extend Igusa’s stationary phase method to this type of exponential sums. We also study the number of solutions of a polynomial congruence along the points of the reduction mod pm of a p-adic analytic submanifold of Zp . In addition,...