Note on a conjecture of Hildebrand regarding friable integers

Régis de la Bretèche, Gérald Tenenbaum

Type: Article

Publication Date: 2023-01-01

Citations: 0

DOI: https://doi.org/10.4064/aa221127-24-4

Abstract

Hildebrand proved that the smooth approximation for the number $\varPsi (x,y)$ of $y$-friable integers not exceeding $x$ holds for $y \gt (\log x)^{2+\varepsilon }$ under the Riemann hypothesis and he conjectured that it fails when $y\leqslant (\log x)^{2

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF

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Works That Cite This (0)

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Works Cited by This (5)

Action	Title	Year	Authors
+	Introduction to Analytic and Probabilistic Number Theory	2015	Gérald Tenenbaum
+	Sur la distribution des nombres premiers	1901	Helge Koch
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan
+	On Integers Free of Large Prime Factors	1986	Adolf Hildebrand Gérald Tenenbaum
+	Smooth integers and the Dickman $ρ$ function	2022	Ofir Gorodetsky