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200?), Small gaps between products of two primes
- arXiv.math.NT/0609615. GAPS BETWEEN ALMOST PRIMES 23
"... As an approximation to the twin prime conjecture it was proved in [11] that (1.1) liminf n→∞ pn+1 − pn ..."
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As an approximation to the twin prime conjecture it was proved in [11] that (1.1) liminf n→∞ pn+1 − pn
Lower bounds for the number of smooth values of a polynomial, electronic preprint available online at http://xxx.lanl.gov/abs/math.NT/9807102
, 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 ..."
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Cited by 2 (1 self)
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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.
