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February 21, 2008

Benjamin Fine, Gerhard Rosenberger – Number Theory An Introduction Via The Distribution of Primes

Section 4.2 Chebychev’s Estimate and Some Consequences. (p.136ff)

Version in the book: $\displaystyle \frac{Log(2)}{4}\frac{x}{Log{(x)}}<\pi(x)<32Log(2)\frac{x}{Log(x)}$

Section 4.6 The Prime Number Theorem – The Elementary Proof (p.180ff)

Jeffrey Stopple – A Primer of Analytic Number Theory

Section 5.2 Chevyshev’s Estimates

Version in the book: $\displaystyle \frac12\frac{x}{Log{(x)}}<\pi(x)<2\frac{x}{Log{(x)}}, (x>15)$

http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf

http://en.wikipedia.org/wiki/Prime_number_theorem

Sylvester’s Papers: http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath&idno=AAS8085

May 22, 2007

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