Details

Autor(en) / Beteiligte

• Panario, Daniel
• Gourdon, Xavier
• Flajolet, Philippe
• Buhler, Joe P.

Titel

An analytic approach to smooth polynomials over finite fields

Ist Teil von

• Algorithmic Number Theory, 2006, p.226-236

Ort / Verlag

Berlin, Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2006

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider the largest degrees that occur in the decomposition of polynomials over finite fields into irreducible factors. We expand the range of applicability of the Dickman function as an approximation for the number of smooth polynomials, which provides precise estimates for the discrete logarithm problem. In addition, we characterize the distribution of the two largest degrees of irreducible factors, a problem relevant to polynomial factorization. As opposed to most earlier treatments, our methods are based on a combination of exact descriptions by generating functions and a specific complex asymptotic method.