An analytic approach to smooth polynomials over finite fields

An analytic approach to smooth polynomials over finite fields (1998)

by Daniel Panario , Xavier Gourdon

Venue:	in Algorithmic Number Theory: Third Intern. Symp., ANTS-III
Citations:	5 - 1 self

Datum	Value	Source
TITLE	An analytic approach to smooth polynomials over finite fields	INFERENCE
AUTHOR NAME	Daniel Panario	SVM HeaderParse 0.2
AUTHOR AFFIL	1 Department of Computer Science, University of Toronto,	SVM HeaderParse 0.2
AUTHOR ADDR	M5S 3G4, Toronto, Canada	SVM HeaderParse 0.2
AUTHOR NAME	Xavier Gourdon	SVM HeaderParse 0.2
AUTHOR AFFIL	1 Department of Computer Science, University of Toronto,	SVM HeaderParse 0.2
AUTHOR ADDR	M5S 3G4, Toronto, Canada	SVM HeaderParse 0.2
ABSTRACT	Abstract. We consider the largest degrees that occur in the decomposi-tion 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 dis-tribution of the two largest degrees of irreducible factors, a problem relevant to polynomial factorization. As opposed to most earlier treat-ments, our methods are based on a combination of exact descriptions by generating functions and a specific complex asymptotic method. 1	SVM HeaderParse 0.2
YEAR	1998	INFERENCE
VENUE	in Algorithmic Number Theory: Third Intern. Symp., ANTS-III	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	226--236	INFERENCE
VOLUME	1423	INFERENCE
CITATIONS	15 found	ParsCit 1.0