Heath-Brown, D. R. The square sieve and consecutive square-free numbers. (English) Zbl 0514.10038 Math. Ann. 266, 251-259 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 14 ReviewsCited in 49 Documents MSC: 11N35 Sieves 11N05 Distribution of primes Keywords:square sieve; consecutive pairs of square-free integers Citations:Zbl 0368.10038 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Carlitz, L.: On a problem in additive arithmetic. Quart. J. Math. Oxford Ser.3, 273-290 (1932) · JFM 58.0185.01 · doi:10.1093/qmath/os-3.1.273 [2] Erdös, P., Szekeres, G.: Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem. Acta Sci. Math. Szeged7, 95-102 (1935) · JFM 60.0893.02 [3] Gallagher, P.X.: A larger sieve. Acta Arith.18, 77-81 (1971) · Zbl 0231.10028 [4] Hayes, D.: Character sums over finite fields. (unpublished) [5] Hooley, C.: On the representations of a number as the sum of four cubes: I. Proc. London Math. Soc. (3)36, 117-140 (1978) · Zbl 0368.10038 · doi:10.1112/plms/s3-36.1.117 [6] Iwaniec, H.: A new form of the error term in the linear sieve. Acta Arith.37, 307-320 (1980) · Zbl 0444.10038 [7] Montgomery, H.L.: Topics in multiplicative number theory. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0216.03501 [8] Shiu, P.: A Brun-Titchmarsh theorem for multiplicative functions. J. reine angew. Math. Math.313, 161-170 (1980) · Zbl 0412.10030 · doi:10.1515/crll.1980.313.161 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.