(adsbygoogle = window.adsbygoogle || []).push({}); "Correspondence" principle?..

let be the Zeta function defined for twin primes:

[tex] Z(s)=\prod (1-p^{-s})^{-1} [/tex] s>1

Where the product is taken only over twin primes so p and p+2 are primes..then my question is if we can define the Chebshev functions for twin primes [tex] \psi_2 (x) [/tex] [tex] \theta_2 (x) [/tex] in the form:

[tex] \theta ' _2 (x) = \pi '_2 (x)log(x) [/tex]

[tex] \frac{Z'(s)}{Z(s)}=s\int_{0}^{\infty}dx\psi _2 (x) x^{-s-1} [/tex]

the "correspondence2 principle in Number Theory would mean that we can define analogue functions for twin primes and normal primes....

Where Pi2(x) is the density of twin primes... if also is satisfied that:

[tex] \psi _2(x)- \theta _2 (x) =0 [/tex] when x--->oo an asymptotic formula for twin primes density can be given.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Correspondence principle?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Correspondence principle | Date |
---|---|

I Is there a ket to correspond to every bra? | Jan 14, 2018 |

I Intuition behind elementary operations on matrices | May 20, 2017 |

I Maximal Ideals and the Correspondence Theorem for Rings | Aug 31, 2016 |

Corollary to Correspondence Theorem for Modules | Nov 5, 2015 |

Eigenvalues/vectors of Hermitian and corresponding unitary | Jan 22, 2015 |

**Physics Forums - The Fusion of Science and Community**