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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the distribution of the number of prime factors of sums $a+b$
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by P. Erdős, H. Maier and A. Sárközy PDF
Trans. Amer. Math. Soc. 302 (1987), 269-280 Request permission

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
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 269-280
  • MSC: Primary 11N60
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0887509-X
  • MathSciNet review: 887509