4 papers
An Algebraic Approach to the Fundamental Theorem of Algebra
Priyabrata Mandal, Sajad A. Sheikh
In this paper, we investigate the algebraic counterpart of the Fundamental Theorem of Algebra. We explore the concept of real closed fields and quadratic forms. We show, by means o…
Finite-Degree Probabilistic Zero Certificates for Random Polynomials
Sajad A. Sheikh
Classical zero-localization theorems give deterministic certificates that all zeros of a polynomial lie in a prescribed disk, annulus, or related region. When the coefficients are…
Probabilistic Zero Bounds of Certain Random Polynomials
Sajad A. Sheikh, Mohammad Ibrahim Mir
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coeffic…
On Average Modulus of Random Polynomials Over a Unit Circle and Disc
Sajad A. Sheikh, Mohd. Ibrahim Mir
This article presents some interesting and novel results concerning the average modulus of random polynomials on the unit circle and the unit disc, with coefficients distributed as…