%0 Book Section %1 noKey %A Panario, Daniel %A Gourdon, Xavier %A Flajolet, Philippe %B Algorithmic Number Theory %D 1998 %E Buhler, JoeP. %I Springer Berlin Heidelberg %K Polynomapproximation endlische_Körper %P 226-236 %R 10.1007/BFb0054865 %T An analytic approach to smooth polynomials over finite fields %U http://dx.doi.org/10.1007/BFb0054865 %V 1423 %X 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. %@ 978-3-540-64657-0

@incollection{noKey, abstract = {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.}, added-at = {2014-01-07T12:23:27.000+0100}, author = {Panario, Daniel and Gourdon, Xavier and Flajolet, Philippe}, biburl = {https://www.bibsonomy.org/bibtex/22ba0abeb282273f3b4ca06ad0c0db970/keinstein}, booktitle = {Algorithmic Number Theory}, doi = {10.1007/BFb0054865}, editor = {Buhler, JoeP.}, interhash = {bdcc0f050e3836608def7fae624dccaf}, intrahash = {2ba0abeb282273f3b4ca06ad0c0db970}, isbn = {978-3-540-64657-0}, keywords = {Polynomapproximation endlische_Körper}, pages = {226-236}, publisher = {Springer Berlin Heidelberg}, series = {Lecture Notes in Computer Science}, timestamp = {2014-01-07T12:23:27.000+0100}, title = {An analytic approach to smooth polynomials over finite fields}, url = {http://dx.doi.org/10.1007/BFb0054865}, volume = 1423, year = 1998 }