Additive complexity and roots of polynomials over number fields and p-adic fields Conference Paper uri icon


  • Springer-Verlag Berlin Heidelberg 2002. Consider any nonzero univariate polynomial with rational coefficients, presented as an elementary algebraic expression (using only integer exponents). Letting (f) denotes the additive complexity of f, we show that the number of rational roots of f is no more than 15 + (f)2(24.01)(f)(f)!. This provides a sharper arithmetic analogue of earlier results of Dima Grigoriev and Jean-Jacques Risler, which gave a bound of C(f)2 for the number of real roots of f, for (f) sufficiently large and some constant C with 1

published proceedings


author list (cited authors)

  • Rojas, J. M.

citation count

  • 3

complete list of authors

  • Rojas, JM

publication date

  • January 2002