WebSMOOTH VALUES OF THE ITERATES OF THE EULER’S PHI-FUNCTION Youness Lamzouri Abstract. Let `(n) be the Euler-phi function, deflne `0(n) = n and `k+1(n) = `(`k(n)) for all k ‚ 0. We will determine an asymptotic formula for the set of integers n less than x for which `k(n) is y-smooth, conditionally on a weak form of the Elliott-Halberstam … WebThe Granville set. In 1996, Andrew Granville proposed the following construction of a set: Let , and for any integer larger than 1, let if , <,. A Granville number is an element of for …
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WebAug 26, 2015 · Theorem 2allows us to show the existence of many X" smooth numbers in intervals of length p X. Alternatively we could have deduced this from Theorem 1using ideas of Croot [4] (building on earlier work of Friedlander and Granville [9]). Corollary 1. Let ">0 be given. There exists a positive constant C(") WebAndrew Granville: Smooth numbers II Noriko Yui: Congruent number problems in dimension one and two Henri Cohen: Computational class field theory Clay Mathematics … easy english muffins recipe microwave
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WebFeb 23, 2016 · Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers - Volume 152 Issue 6 Skip to main content Accessibility help We use … WebNov 1, 2015 · A. Granville. Smooth numbers: computational number theory and beyond. Algorithmic Number Theory, MSRI Publications, vol. 44 (2008), pp. 267-323. View in Scopus Google Scholar [10] B. Harris, L. Schoenfeld. Asymptotic expansions for the coefficients of analytic generating functions. WebNov 29, 2024 · Harper, A., Bombieri–Vinogradov and Barban–Davenport–Halberstam type theorems for smooth numbers. Preprint.Google Scholar. 8 Hildebrand, A., Integers free of large prime divisors in short intervals. ... Granville, Andrew and Shao, Xuancheng 2024. Bombieri-Vinogradov for multiplicative functions, ... easy english news pdf