The linear cubic $p$-adic recurrence and its value function

P -adic root separation for quadratic and cubic polynomials

We study p-adic root separation for quadratic and cubic polynomials with integer coefficients. The quadratic and reducible cubic polynomials are completely understood, while in the irreducible cubic case, we give a family of polynomials with the bound which is the best currently known.

Multivariate P-adic L-function

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...

The “missing” p-adic L-function – DRAFT

One Dimensional p-adic Integral Value Transformations

In this paper, a set of transformations is defined on to. Some basic and naïve mathematical structure of is introduced. The concept of discrete dynamical systems through IVT and some further research scope of IVTs are highlighted. and 4]. A class of discrete transformations on named as Integral Value Transformations (IVT), corresponding to each of those CA rules, is introduced in the formation ...

VALUATIONS OF p-ADIC REGULATORS OF CYCLIC CUBIC FIELDS

We compute the p-adic regulator of cyclic cubic extensions of Q with discriminant up to 1016 for 3 < p < 100, and observe the distribution of the p-adic valuation of the regulators. We find that for almost all primes the observation matches the model that the entries in the regulator matrix are random elements with respect to the obvious restrictions. Based on this random matrix model a conject...