Can a differential equation for [tex] \pi (x) [/tex] (prime number counting function ) exist?..for example of the form :grumpy: :grumpy:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] f(x)y'' +g(x)y' +h(x)y = u(x) [/tex] where the functions f,g,h and u

are known, and with the initial value problem [tex] y(2)= 0 [/tex] for example....or is there any theorem forbidding it?..

By the way do you Number theoritis use Numerical methods ? (to solve diophantine equations, or Integral equations of first kind involving important functions) that,s all...

-In fact for every Green function of Any operator if we put:

[tex] \sum_ p L[G(x,p)] = \pi ' (x) [/tex] :uhh: :uhh: the problem is if some valuable info can be obtained from here

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# Differential equation for Pi(x)

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