✦ LIBER ✦

Diophantine Inequalities for Polynomial Rings

✍ Scribed by Chih-Nung Hsu

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 165 KB
Volume: 78
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2390

No coin nor oath required. For personal study only.

✦ Synopsis

We study the Hardy Littlewood method for the Laurent series field F q ((1ÂT )) over the finite field F q with q elements. We show that if * 1 , * 2 , * 3 are non-zero elements in F q ((1ÂT )) satisfying * 1 Â* 2 Â F q (T ) and sgn(* 1 )+sgn(* 2 )+sgn(* 3 )=0, then the values of the sum * 1 P 1 +* 2 P 2 +* 3 P 3 , as P i (i=1, 2, 3) run independently through all monic irreducible polynomials in F q [T ], are everywhere dense on the ``non-Archimedean'' line F q ((1ÂT )), where sgn( f ) # F q denotes the leading coefficient of f # F q ((1ÂT )).

📜 SIMILAR VOLUMES

Diophantine definitions for some polynom

Diophantine definitions for some polynomial rings

✍ Alexandra Shlapentokh 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 499 KB

An Inequality for Cosine Polynomials

✍ Horst Alzer 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 113 KB

Some Sharp Inequalities for Algebraic Po

Some Sharp Inequalities for Algebraic Polynomials

✍ Semyon Rafalson 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 253 KB

Let H n be the set of all algebraic polynomials with real coefficients of degree at most n(n+1 # N).

A Polynomial Time Algorithm for Diophant

A Polynomial Time Algorithm for Diophantine Equations in One Variable

✍ F CUCKER; P KOIRAN; S SMALE 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 195 KB

We exhibit an algorithm computing, for a polynomial f ∈ Z [t], the set of its integer roots. The running time of the algorithm is polynomial in the size of the sparse encoding of f .

Inequalities for a Polynomial and Its De

Inequalities for a Polynomial and Its Derivative II

✍ K.K. Dewan 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 98 KB

Stechkin–Marchaud-Type Inequalities for

Stechkin–Marchaud-Type Inequalities for Baskakov Polynomials

✍ Shunsheng Guo; Hongzhi Tong; Gengsheng Zhang 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 118 KB

shows some Stechkin-Marchaud-type inequalities in connection with Bernstein polynomials. In this paper, we introduce w 2 j l (f, t) a, b , and give the Stechkin-Marchaud-type inequalities for Baskakov polynomials.