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

abstract

• 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

authors

• Rojas, Joseph

published proceedings

• ALGORITHMIC NUMBER THEORY

author list (cited authors)

• Rojas, J. M.

citation count

• 3

complete list of authors

• Rojas, JM

publication date

• January 2002

publisher

• Springer Nature  Publisher

published in

• Lecture Notes in Computer Science  Journal

keywords

• 46 Information And Computing Sciences

Digital Object Identifier (DOI)

• 10.1007/3-540-45455-1_39

International Standard Book Number (ISBN) 10

• 3-540-43863-7

International Standard Book Number (ISBN) 13

• 9783540438632

start page

• 506

end page

• 515

volume

• 2369

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2F3-540-45455-1_39