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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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