On polynomials with positive coefficients
نویسندگان
چکیده
منابع مشابه
Roots of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
متن کاملOn the distribution of coefficients of powers of positive polynomials
Using the formalism of polynomials with positive coefficients, the fact that exactly half of all subsets of a finite set have even cardinality can be generalized asymptotically. The well-known fact that every finite nonempty set has as many subsets of even cardinality as of odd cardinality can be restated as follows. If d denotes the particular integer 2, then for any integers 0 ≤ j ≤ d − 1, n ...
متن کاملDistribution of zeros of polynomials with positive coefficients
We describe the limit zero distributions of sequences of polynomials with positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.
متن کاملPolynomials with Nonnegative Coefficients
The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen's inequality. The conjecture was also made independ...
متن کاملOn Cyclotomic Polynomials with ± 1 Coefficients
We characterize all cyclotomic polynomials of even degree with coefficients restricted to the set {+1,−1}. In this context a cyclotomic polynomial is any monic polynomial with integer coefficients and all roots of modulus 1. Inter alia we characterize all cyclotomic polynomials with odd coefficients. The characterization is as follows. A polynomial P (x) with coefficients ±1 of even degree N − ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1988
ISSN: 0021-9045
DOI: 10.1016/0021-9045(88)90119-0