--- In

primenumbers@yahoogroups.com, Jose RamÃ³n Brox <ambroxius@t...>

wrote:

> A pseudo zeta function and the distribution of primes:

>

> http://www.pnas.org/cgi/content/full/97/14/7697?

maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&searchid=1043940786913_2887&s

tored_search=&FIRSTINDEX=20&tocsectionid=Mathematics

>

> Regards. Jose Brox.

>

>

Thanks for posting this, it is indeed very interesting!!

The statement that caught my eye is a few lines above equation [4].

In Equation [2] the prime zeta function phi(s) is defined.

Then before [4] he states:

" hence the Riemann hypothesis is equivalent to the claim that phi(s)

can be analytically continued into the strip 1/2 < Re s <1."

Now as I mentioned in an earlier posting, Carl-Erik Froberg in his

1968 paper "On The Prime Zeta Function" makes the statement in his

introduction, after defining P(s) as the prime zeta function:

"In the next section we shall show that P(s) can be expressed as an

infinite series involving the usual Riemann zeta function.

Simultaneously, this formula provides an analytic continuation to the

strip 0 < sigma <= 1."

If indeed both of these statements are correct and agree in their

definition of analytic continuation, this I belive would imply a

proof of Riemann's hypothesis. Unfortuneately Froberg gives no

justification of the second sentence, while the first refers to the

usual mobius and log sum which is given.

If what I've written above makes sense and isn't all fluff, then I

would strongly suggest that someone check one of

Landau-Walfisz, Rend. di Palermo 44 (1919), p. 82-86

Glaisher, Quart. Jour. of Math. 25 (1891), p. 347

C.W. Merrifield, The sums of the series of reciprocals of the

prime numbers and of their powers, Proc. Roy. Soc. London, (1881),

vol. 33, p. 4-10

and see if these are where Froberg makes his assertions from. Perhaps

I should email Froberg directly? (A google search shows he is still

working in Sweden at at Lund University and Lund Institute of

Technology)

Thanks,

Andrew Walker