Let be the prime-counting function and be a non-constantrationalfunction. Can we have for infinitely many values of ?

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- Oct 24th 2009, 06:17 PMNonCommAlgPrime-counting function
Let be the prime-counting function and be a non-constant

*rational*function. Can we have for infinitely many values of ? - Oct 24th 2009, 11:34 PMchisigma
A 'rational function' can be written as...

(1)

... where and are polynomial in x of degree n and m so that we can write...

(2)

... or equivalently...

(3)

At the end of nineteenth century it has been demonstrated that is...

(4)

... or equivalently...

(5)

Combining (3) and (5) we find that is...

(6)

... so that the situation described by NCA is impossible...

Kind regards

- Oct 25th 2009, 01:10 AMNonCommAlg