Consecutive integers with no large prime factors (1976)

by R B Eggleton, J L Selfridge
Venue:J. Austral. Math. Soc. Ser. A
Add To MetaCart
Results 1 - 1 of 1

Lower bounds for the number of smooth values of a polynomial, electronic preprint available online at http://xxx.lanl.gov/abs/math.NT/9807102

by Greg Martin , 1998
"... Abstract. We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound the number of smooth values of a polynomial from above, a corresponding lower bound of the co ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
Abstract. We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound the number of smooth values of a polynomial from above, a corresponding lower bound of the correct order of magnitude has hitherto been established only in a few special cases. The purpose of this paper is to provide such a lower bound for an arbitrary polynomial. Various generalizations to subsets of the set of values taken by a polynomial are also obtained. 1.