On Reduced Weighted Bombieri \(l_2\)-Norm
Abstract
In this article, P is a given polynomial with real coefficients.Our aim is to study, with various normalisations on the polynomial Q with real coefficients, the quantity inf [P Q] 2 .When Q is monic orthis quantity is known as the reduced weighted Bombieri l2-norm of P and denoted by [P ].On the other hand if Q is monic and Q(0) ≥ 1, it is denoted by [P ] 0 .More precisely we study some properties of these norms and give bounds on the ratio [P ] 0 [P ] 0 under certain conditions on the roots of P .2020 Mathematics Subject Classification.11Y99,
Fields of Study & Subjects
Mathematical functions and polynomials
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Asia Pacific Journal of Mathematics
- Volume
- 13
- Pages
- 20–20
- Publication date
- 1 January 2026
- Language
- EN