Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I'm calculating the roots of the function \begin{equation} R(x) = \sum_{k=1}^{\infty}\frac{\mu(k)}{k}li(x^{1/k}) \end{equation} This function seems to have a largest and smallest positive root. Can anyone tell me if the roots of $R(x)$ have any significance for the prime counting function?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Not that I know of. If you have not already, see the paper by Folkmar Bornemann that describes a method for finding the roots of R(x) (see link below). It's a very interesting method.

Best regards,

Tom

Paper

share|improve this answer
    
The first lemma of this paper seems to making the assumption that the zeros of the zeta-function are all simple (without explicitly stating it). –  Micah Milinovich Sep 16 '10 at 23:08
    
Okay. Thank you very much. –  alext87 Sep 17 '10 at 7:09

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.