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In section 2.4 of the book "Riemann's zeta function" by Edwards, the estimate $n(R)\leq 2R\log(R)$ is derived, where $n(R)$ is the number of roots of the equation $\xi(\rho)=0$ inside the circle $|s-1/2|=R$. But the last line of the proof is $$n(R)\leq \frac{2}{\log 2}R \log R +2R -\frac{\xi(1/2)}{\log 2}\leq 2R \log R$$ and the second inequality is not true for large $R$. It would become true by replacing $2R\log R$ with $3R\log R$. Is this a typo in the book, or am I missing something?

Math101
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    My version (copyright 1974, Dover edition first published in 2001) says $\le 3,R,log,R$. Which version do you have? – Steven Clark Oct 16 '21 at 16:21
  • @Steven Clark Interesting...mine is also copyright 1974, but it's Academic Press, published 1974. Obviously they corrected the error in a subsequent printing...In any case thanks for letting me know. – Math101 Oct 17 '21 at 00:12

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