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Physical Sciences and Mathematics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
A Sequence Of Polynomials For Approximating Arctangent, Herbert A. Medina
A Sequence Of Polynomials For Approximating Arctangent, Herbert A. Medina
Mathematics Faculty Works
No abstract provided.
Integral Points Of Small Height Outside Of A Hypersurface, Lenny Fukshansky
Integral Points Of Small Height Outside Of A Hypersurface, Lenny Fukshansky
CMC Faculty Publications and Research
Let F be a non-zero polynomial with integer coefficients in N variables of degree M. We prove the existence of an integral point of small height at which F does not vanish. Our basic bound depends on N and M only. We separately investigate the case when F is decomposable into a product of linear forms, and provide a more sophisticated bound. We also relate this problem to a certain extension of Siegel’s Lemma as well as to Faltings’ version of it. Finally we exhibit an application of our results to a discrete version of the Tarski plank problem.
On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain
On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain
Turkish Journal of Mathematics
In this note, we improve upon Cauchy's classical bound, and upon some recent bounds for the moduli of the zeros of a polynomial.