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VOL. 84 | 2020 An asymptotic formula and some explicit estimates of the counting function of $y$-friable numbers
Biswajyoti Saha, Ayyadurai Sankaranarayanan, Yuta Suzuki

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Abstract

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.

Information

Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283194

Digital Object Identifier: 10.2969/aspm/08410367

Subjects:
Primary: 11N25, 11N37

Rights: Copyright © 2020 Mathematical Society of Japan

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