On the distribution of the number of prime factors of sums
Authors:
P. Erdős, H. Maier and A. Sárközy
Journal:
Trans. Amer. Math. Soc. 302 (1987), 269280
MSC:
Primary 11N60
MathSciNet review:
887509
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Abstract: We continue a series of investigations by A. Balog and two of the authors (P. Erdös and A. Sárközy) on the arithmetic properties of the elements , where , , and "dense sequences." The present paper transfers the famous ErdösKac theorem on the normal distribution of the number of distinct prime factors of integers to such "sum sequences."
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MR 764627
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I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Interscience, New York, 1954.
 [1]
 A. Balog and A. Sárközy, On sums of sequences of integers. III, Acta Math. Acad. Sci. Hungar. 44 (1984), 339349. MR 764627 (86g:11056c)
 [2]
 P. D. T. A. Elliott, Probabilistic number theory. II, SpringerVerlag, 1980. MR 560507 (82h:10002b)
 [3]
 J. Erdös and M. Kac, The Gaussian law of errors in the theory of additive numbertheoretic functions, Amer. J. Math. 62 (1940), 738742. MR 0002374 (2:42c)
 [4]
 P. Erdös and A. Sárközy, On divisibility properties of integers of the form , Acta. Math. Acad. Sci. Hungar. (to appear).
 [5]
 K. Prachar, Primzahlverteilung, SpringerVerlag, 1957. MR 0087685 (19:393b)
 [6]
 R. A. Rankin, The difference between consecutive prime numbers, J. London Math. Soc. 13 (1938), 242247.
 [7]
 A. Sárközy, On the number of prime factors of integers of the form , Studia Sci. Math. Hungar. (to appear).
 [8]
 A. Sárközy and C. L. Stewart, On divisors of sums of integers. II, J. Reine Angew. Math. 365 (1986), 171191. MR 826157 (88f:11088)
 [9]
 I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Interscience, New York, 1954.
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DOI:
http://dx.doi.org/10.1090/S0002994719870887509X
PII:
S 00029947(1987)0887509X
Article copyright:
© Copyright 1987
American Mathematical Society
