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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Estimate for de Bruijn function with small fixed smoothness bound
This is discussed in chapter III.5 of Tenenbaum Intro to analytic and probabilistic number theory (Cambridge, 1995). The estimate up to a factor $1+O(B^2/\log x\log B)$ uniform in $2 \le B \le \sqrt{ …