## Abstract Let ‖ · ‖ denote the uniform norm in the unit disk of the complex plane ℂ. The main result in this note is as follows: __For any complex polynomial P of degree at most n and any α__ ∈ ℂ __the inequality__ ‖__P__ ‖ ⩽ (__n__ + 1)(‖__z P__ (__z__) + __α__ ‖ ‐ |__α__ |) __holds.__ For any
Estimation of Norms of Multivariate Polynomials with Integral Coefficients
✍ Scribed by Francisco Luquin; Concepción Besga
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 167 KB
- Volume
- 96
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
Using Fekete's method we obtain estimates for the L p -norms of minimal integral generalized multivariate polynomials. We particularize these estimates for the cases of ordinary polynomials and quasi-polynomials. We also show the existence of a limit in the minimal quadratic deviations from zero for univariate integral polynomials.
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