Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields

Details Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields

2002-01-16

arxiv.org/abs/math/0201154v2

Mathematics

Number Theory

9 pages, no figures, requires llncs.cls (included) to compile. This version has a slight title change, includes new clarificat

Scientific paper

Consider any nonzero univariate polynomial with rational coefficients, presented as an elementary algebraic expression (using only integer exponents). Letting sigma(f) denotes the additive complexity of f, we show that the number of rational roots of f is no more than 15 + sigma(f)^2 (24.01)^{sigma(f)} sigma(f)!. This provides a sharper arithmetic analogue of earlier results of Dima Grigoriev and Jean-Jacques Risler, which gave a bound of C^{sigma(f)^2} for the number of real roots of f, for some constant C with 1

Affiliated with

Also associated with

No associations

Rating

Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484549