[seqfan] A strong estimate of w(2n) from below and above

[Tomasz Ordowski]

Dear readers!

Let w(m) = (1 - t(m)) / (1 + t(m)),
where t(m) = zeta(2m) / zeta(m)^2.

For m = 2n, we have on the OEIS:
w(2n) = A348829(n) / A348830(n),
t(2n) = A114362(n) / A114363(n).

Conjecture:
0 < w(2n) - (1/2^{2n}+1/3^{2n}+1/5^{2n}+1/7^{2n}) < 1/11^{2n},
for every n > 0.

Amiram Eldar confirmed my strong estimate up to n = 10^4.

Is this conjecture provable?

Best regards,

Thomas Ordowski
_______________________
The strong estimate of w(2n) from below and above:
Sum_{prime p <= 7} 1/p^{2n} < w(n) < Sum_{prime p <= 11} 1/p^{2n},
for every n > 0.