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The distribution of smooth numbers in arithmetic progressions


Authors: Antal Balog and Carl Pomerance
Journal: Proc. Amer. Math. Soc. 115 (1992), 33-43
MSC: Primary 11N25; Secondary 11L05, 11N36
DOI: https://doi.org/10.1090/S0002-9939-1992-1089401-4
MathSciNet review: 1089401
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Abstract: We estimate the number of integers $ n$ up to $ x$ in the arithmetic progression $ a(\bmod q)$ with $ n$ free of prime factors exceeding $ y$. For a wide range of the variables $ x,y,q$, and $ a$ we show that this number is about $ x/(q{u^u})$, where $ u = \log x/\log y$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1089401-4
Article copyright: © Copyright 1992 American Mathematical Society

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