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For automorphisms of a polynomial ring in two variables over a domain R, we show that local tameness implies global tameness provided that every 2-generated invertible R-module is free. We give many e...
A note on computational complexities of polynomial type
computational complexities polynomial type
2010/11/18
We introduce a notion of a polynomial type complexity of a multivariate polynomial. We provide examples of polynomial type complexities, including the determinantal complexity. We present two algorit...
Polynomial estimates for c-functions on reductive symmetric spaces
Polynomial c-functions reductive symmetric spaces
2010/11/8
The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.
On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields
The Characteristic Polynomial Frobenius Supersingular Abelian
2010/11/15
In this article, we derive the list of the characteristic polynomials of the Frobenius endomorphism of simple supersingular abelian varieties of dimension $1,~2,~3,~4,~5,~6,~7$ over $\mathbb{F}_q$ whe...
Polynomial Approximation in Sobolev Spaces on the Unit Sphere and the Unit Ball
Polynomial Sobolev Spaces Unit Sphere Unit Ball
2010/11/18
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial ap...
An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem
the Polynomial Matrix Spectral Factorization Theorem
2010/11/22
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and lin...
alphaCertified: certifying solutions to polynomial systems
alphaCertified certifying polynomial systems
2010/11/11
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial syste...
Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves
Topological recursion Poincare polynomial combinatorial moduli space of curves
2010/12/3
We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satis es a topological
recursion formu...
Integer Sequences associated with Integer Monic Polynomial
Integer Sequences Integer Monic Polynomial
2010/10/29
To every integer monic polynomial of degree m can be associated m integer sequences having interesting properties to the roots of the polynomial. These sequences can be used to find the real roots of...