We describe an algorithm for solving systems of univariate p-adic constraints. In analogy with univariate real constraints, we formalize univariate p-adic constraints as univariate polynomial equations and order comparisons between p-adic values of univariate polynomials. Systems of constraints are arbitrary boolean combinations of such constraints. Our method combines techniques of Presburger ...

In this work we describe the use of truncated p adic expansion for handling rational numbers by parallel algorithms for symbolic computation As a case study we propose a parallel implementation for solving linear systems over the rationals The parallelization is based on a multiple homomorphic image technique and the result is recovered by a parallel version of the Chinese remainder algorithm U...

In this paper, we introduce q-analogues of degenerate Catalan numbers and polynomials with the help a fermionic p-adic q-integrals on Zp establish some new connections Stirling first second kinds. Furthermore, also find few identities results type numbers.

We initiate and examine integer powers of the (possibly unbounded) diagonal operators on the so-called p-adic Hilbert space Eω (see [10], [11], and [3]). For that, we first give and recall the required background on author’s recent work related to the formalism of unbounded linear operators in the p-adic setting [5]. Next, we shall be dealing with integer powers of the diagonal operators, their...

In quantum-mechanical experiments, as well as in all measurements, numerical results belong to the field of rational numbers Q. In principle, the corresponding theoretical models could be made using only Q, but it would missed usual effectiveness and beauty of mathematical analysis. So, instead of Q one traditionally applies the field of real numbers R in classical mechanics and the field of co...

We define a p-adic character to be a continuous homomorphism from 1 + tFq [[t]] to Zp. For p > 2, we use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in Zq , indexed by natural numbers relatively prime to p, and for which limi→∞ ci = 0. To such a p-adic character we associate an L-function, and we prove that this L-f...

We report on our project to find explicit examples of K3 surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are p-adic in nature.

The function ez shows that a complex entire function can indeed omit one value. Lately, it has become fashionable to prove p -adic versions of value distribution theorems, of which Picard’s Theorem is an example, though not a recent one. More recent examples can be found in the works listed in the references section. Recall that the p -adic absolute value | |p on the rational number field Q is ...