Characteristic Polynomials of p-adic Matrices
نویسندگان
چکیده
We analyze the precision of the characteristic polynomial χ(A) of an n × n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p), we give a criterion (checkable in time O (̃n)) for χ(A) to have precision exactly O(p). We also give a O (̃n) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p).
منابع مشابه
Higher Order Degenerate Hermite-Bernoulli Polynomials Arising from $p$-Adic Integrals on $mathbb{Z}_p$
Our principal interest in this paper is to study higher order degenerate Hermite-Bernoulli polynomials arising from multivariate $p$-adic invariant integrals on $mathbb{Z}_p$. We give interesting identities and properties of these polynomials that are derived using the generating functions and $p$-adic integral equations. Several familiar and new results are shown to follow as special cases. So...
متن کاملField of Characteristic Zero
Let K be a p-adic field of characteristic zero. For polynomials A,B ∈ K[x] we consider decompositions A(x)f(x) +B(x)g(x) = 1 of entire functions f, g on K and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. Also, an independent proof of a p-adic diophantic statement due to D. N. Clark is given.
متن کاملDeterminants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
متن کاملSymmetry classes of polynomials associated with the dihedral group
In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.
متن کاملModified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017