Alexandr Martinevski

The Chebyshev–Monomial Oscillation Gap: Contact Geometry, Level Sets, and Gaussian Crossovers

We study the uniform norm of a prescribed Chebyshev polynomial against a monomial, \(\|T_m-x^d\|_{\infty,[-1,1]}\), for integers \(d\ge m\ge3\) of matching parity. The continuous contact surface \(\mathcal{C}(p,q)=\max_{0\le\theta\le\pi/2} |\cos^p\theta-\cos(q\theta)|\) separates...

Critical values, resultants and norms of the Chebyshev defect

For \(d\ge3\) let \(F_d(c)=c^d-T_d(c)\) and let \(C_d\) be its uniform norm on \([-1,1]\). We connect the critical geometry of this defect with a single cyclotomic resultant. The critical values at distinct positive critical points have distinct absolute values; a pair of monoton...

Rational moment algebras: spectral reconstruction, factorization and arithmetic rigidity

We consider rational characteristic functions that admit finite symmetric Laplace-mixture representations with simple poles and positive residues. Such positivity does not by itself imply rational factorization; moment rank and rational splitting remain different properties. A ge...

A sharp universal profile for multivariate characteristic-function factorization

We study the maximal factorization defect of characteristic functions for several random blocks. For prescribed moduli of the marginal characteristic-function values, we determine the exact extremal profile, and by optimizing it obtain the sharp universal constant \[ C_d=\max_{0\...

CHEBYSHEV–LUCAS CRITICAL POLYNOMIALS: LOCAL BLOCKS, IRREDUCIBILITY AND GALOIS GROUPS

e introduce and study a family of critical polynomials arising naturally from the maximization problem for the sharp characteristic-function dependence constant \(C_d\). The critical equation for the optimizer admits equivalent Chebyshev and Lucas formulations and leads to a dist...