Displaying similar documents to “Bounds on ternary cyclotomic coefficients”

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

Akritas, Alkiviadis, Argyris, Andreas, Strzeboński, Adam (2008)

Serdica Journal of Computing

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In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental...

Lower Bounds on the Directed Sweepwidth of Planar Shapes

Markov, Minko, Haralampiev, Vladislav, Georgiev, Georgi (2015)

Serdica Journal of Computing

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We investigate a recently introduced width measure of planar shapes called sweepwidth and prove a lower bound theorem on the sweepwidth.

Heights, regulators and Schinzel's determinant inequality

Shabnam Akhtari, Jeffrey D. Vaaler (2016)

Acta Arithmetica

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We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields. ...

On the magnitudes of some small cyclotomic integers

Frederick Robinson, Michael Wurtz (2013)

Acta Arithmetica

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We prove the last of five outstanding conjectures made by R. M. Robinson from 1965 concerning small cyclotomic integers. In particular, given any cyclotomic integer β all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value of one of four explicit types given by two infinite classes and two exceptional cases. We also extend this result by showing that with the addition of one form, the conjecture is true for β with magnitudes...