Root separation for reducible integer polynomials
نویسندگان
چکیده
منابع مشابه
Root separation for reducible integer polynomials
We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
متن کاملRoot separation for irreducible integer polynomials
where the latter limsup is taken over the irreducible integer polynomials P (x) of degree d. A classical result of Mahler [10] asserts that e(d) ≤ d− 1 for all d, and it is easy to check that eirr(2) = e(2) = 1. There is only one other value of d for which e(d) or eirr(d) is known, namely d = 3, and we have eirr(3) = e(3) = 2, as proved, independently, by Evertse [9] and Schönhage [11]. For lar...
متن کاملRoot separation for reducible monic polynomials of odd degree
We study root separation of reducible monic integer polynomials of odd degree. Let H(P ) be the näıve height, sep(P ) the minimal distance between two distinct roots of an integer polynomial P (x) and sep(P ) = H(P )−e(P ). Let er(d) = lim supdeg(P )=d,H(P )→+∞ e(P ), where the limsup is taken over the reducible monic integer polynomials P (x) of degree d. We prove that er(d) ≤ d−2. We also obt...
متن کاملRoot separation for reducible monic quartics
We study root separation for reducible monic integer polynomials of degree four. If H(P ) is the height and sep(P ) the minimal distance between two distinct roots of a separable integer polynomial P (x), and sep(P ) = H(P )−e(P , we show that lim sup e(P ) = 2, where limsup is taken over all reducible monic integer polynomials P (x) of degree 4.
متن کاملReducible cubic CNS polynomials
The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are tr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2014
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa162-4-6