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Transactions of the American Mathematical Society

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On the distribution of the number of prime factors of sums $ a+b$

Authors: P. Erdős, H. Maier and A. Sárközy
Journal: Trans. Amer. Math. Soc. 302 (1987), 269-280
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 $ a + b$, where $ a \in {\mathbf{A}}$, $ b \in {\mathbf{B}}$, $ {\mathbf{A}}$ and $ {\mathbf{B}}$ "dense sequences."

The present paper transfers the famous Erdös-Kac theorem on the normal distribution of the number of distinct prime factors of integers to such "sum sequences."

References [Enhancements On Off] (What's this?)

  • [1] A. Balog and A. Sárközy, On sums of sequences of integers. III, Acta Math. Hungar. 44 (1984), no. 3-4, 339–349. MR 764627,
  • [2] Peter D. T. A. Elliott, Probabilistic number theory. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 240, Springer-Verlag, Berlin-New York, 1980. Central limit theorems. MR 560507
  • [3] P. Erdös and M. Kac, The Gaussian law of errors in the theory of additive number theoretic functions, Amer. J. Math. 62 (1940), 738–742. MR 0002374,
  • [4] P. Erdös and A. Sárközy, On divisibility properties of integers of the form $ a + a'$, Acta. Math. Acad. Sci. Hungar. (to appear).
  • [5] Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0087685
  • [6] R. A. Rankin, The difference between consecutive prime numbers, J. London Math. Soc. 13 (1938), 242-247.
  • [7] A. Sárközy, On the number of prime factors of integers of the form $ {a_i} + {b_j}$, 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), 171–191. MR 826157
  • [9] I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Interscience, New York, 1954.

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Article copyright: © Copyright 1987 American Mathematical Society

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