Talk:Explicit formulae for L-functions: Difference between revisions

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Revision as of 01:33, 30 October 2010

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=== Error? ===

"...Riemann found an explicit formula for the number of primes π(x) less than a given number x."

Should this not be the number of primes '''less than or equal to''' a given number x?

I tried to verify mathematically that the formula gives this, but I am not adept enough to work with it much...I did find that the f(x) formula can work either way (if pi(x) includes x, then f(x) includes x; and if pi(x) excludes x, then f(x) excludes x). This was quite simple using induction.

Besides verifying mathematically, I have always seen the prime counting function before as including x - and it is defined that way on [[Prime-counting function|the Wiki page]].