Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields Institutional Repository Document uri icon


  • 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

author list (cited authors)

  • Rojas, J. M.

complete list of authors

  • Rojas, J Maurice

Book Title

  • arXiv

publication date

  • January 2002