Could the Laplace and Euler Transformations Approximate Pi(x)?

[eljose79]

Here it is a solution for Pi(x) funciton in number thoeroy using the Laplace transformation and Euler,s transformation for alternating series

 

[eljose79]

heop it helps...

 

[Nereid]

I clicked on the link, but got a pop up window asking me if I wanted to open the file or save it. The application also didn't ring any bells with my poor old PC, and my anti-virus software yelled something about not trusting uncertified sources. If it's live in PF I guess it's safe, but what application do I need to view the file with when I do save it?

 

[matt grime]

it's .doc that means word unfortunately. in the math number theory forum he's posted a link to a pdf file at arxiv.

if you want to save the hassle:

synopsis:

something about laplace transforms, which may or may not be true, followed by an approximation cos something's too hard to work out. no indication of the error in the approximation (ie is it asymptotic or what?) followed by an observation that to work out the hard sum requires one to know pi(x) already.

feel free to correct my reading of that of course, i didn't give it my full attention, but that's becuase a skim through revealed serious flaws that the reviewer of the journal undoubtedly saw if it even got that far (papers are often communicated on your behalf by someone else - did you submit it directly?)

 

[HallsofIvy]

Right in the middle we suddenly see
"Now if we could calculate the sum on the left we could apply the Laplace inverse transform to get π(x) unfortunately the sum is hard to calculate so we will seetle for an aproximation of it by using the Euler's transform of an analytical series:"


so that even if everything is correct, this is not π(x) but only another approximation.

By the way, was there a reason for this appearing in the "Phyics" area rather than "Mathematics"?