✦ LIBER ✦

Compositions of Polynomials with Coefficients in a Given Field

✍ Scribed by Alan Horwitz

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 125 KB
Volume: 267
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7778

No coin nor oath required. For personal study only.

✦ Synopsis

Let F ⊂ K be fields of characteristic 0, and let K x denote the ring of polynomials with coefficients in K.

∈ F for some j ≥ 1. Suppose that p ∈ K x , q ∈ K x \F x p not constant. Our main result is that p • q / ∈ F x and D F p • q = D F q . With only the assumption that a n b m ∈ F, we prove the inequality D F p • q ≥ D F q . This inequality also holds if F and K are only rings. Similar results are proven for fields of finite characteristic with the additional assumption that the characteristic of the field does not divide the degree of p. Finally we extend our results to polynomials in two variables and compositions of the form p q x y , where p is a polynomial in one variable.  2002 Elsevier Science (USA)

📜 SIMILAR VOLUMES

Irreducible Polynomials with Coefficient

Irreducible Polynomials with Coefficients in a Complete Discrete Valuation Field

✍ A. Granja 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 397 KB

Counting Polynomials with Zeros of Given

Counting Polynomials with Zeros of Given Multiplicities in Finite Fields

✍ Jean-François Ragot 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 136 KB

We consider the set of polynomials in r indeterminates over a "nite "eld and with bounded degree. We give here a way to count the number of elements of some of its subsets, namely those sets de"ned by the multiplicities of their elements at some points of %P O . The number of polynomials having at l

The Number of Permutation Polynomials of

The Number of Permutation Polynomials of a Given Degree Over a Finite Field

✍ Pinaki Das 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 139 KB

We relate the number of permutation polynomials in F q ½x of degree d q À 2 to the solutions ðx 1 ; x 2 ; . . . ; x q Þ of a system of linear equations over F q , with the added restriction that x i =0 and x i =x j whenever i=j. Using this we find an expression for the number of permutation polynomi

Covariant Quantization of Spinor Fields

Covariant Quantization of Spinor Fields in a Given Gravitational Field

✍ Prof. Dr. sc. Eckhard Kreisel 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 399 KB 👁 1 views

Complex Zeros of Trigonometric Polynomia

Complex Zeros of Trigonometric Polynomials with Standard Normal Random Coefficients

✍ K. Farahmand; A. Grigorash 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 94 KB

In this paper, we obtain an exact formula for the average density of the distribution of complex zeros of a random trigonometric polynomial , where the coefficients η j = a j + ιb j , and a j n j=1 and b j n j=1 are sequences of independent normally distributed random variables with mean 0 and vari

Determination of a crop coefficient for

Determination of a crop coefficient for evapotranspiration in a sparse sorghum field

✍ Tomomichi Kato; Makio Kamichika 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB

## Abstract The FAO basal crop coefficient __K__~__cb__~ and the soil evaporation coefficient __K__~__e__~ for a sparse sorghum field in one growing season were estimated using the compartment model (Shuttleworth–Wallace model; S–W model), which separately estimates transpiration from crops and eva