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An asymptotic formula and some explicit estimates of the counting function of $$y$$-friable numbers. (English) Zbl 1456.11178
Mishou, Hidehiko (ed.) et al., Various aspects of multiple zeta functions – in honor of Professor Kohji Matsumoto’s 60th birthday. Proceedings of the international conference, Nagoya University, Nagoya, Japan August 21–25, 2020. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 84, 367-397 (2020).
Summary: We prove an asymptotic formula for the counting function of $$y$$-friable numbers in a certain range, using the saddle point method. Further, we also prove certain reasonable upper bounds for the counting function of $$y$$-friable numbers for various ranges of $$y$$ whose proofs are comparatively simpler than the earlier ones. Though these bounds need not be the best estimates, these are certainly useful in applications.
For the entire collection see [Zbl 1446.11004].
##### MSC:
 11N25 Distribution of integers with specified multiplicative constraints 11N37 Asymptotic results on arithmetic functions
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