Hi everyone.

Could you plz tell me where the zero's of f(s) in the strip 0 < Re < 1 are ?

Do they all have Re = 1/2 ?

f(s) = 1 - 2^-s - 3^-s + 4^-s - 5^-s + ...

= sum a(n)/n^s

with a(n) = -1 if n = -1 mod 3 or n = -1 mod 4

a(n) = 1 otherwise.

f(s) = zeta(s) - 2 [ 3^-s zeta(s,-1/3) + 4^-s zeta(s,-1/4) - 12^-s zeta(s,-1/12) ]

Could you plz give me some zero's in the strip 0 < Re < 1 ?

Thanks.

Eta.