F(s) = 1/1^s + 0/2^s + 1/3^s + 1/4^s + 0/5^s + 1/6^s + 0/7^s + 1/8^s + ...

The coefficients of this Dirichlet series are the base-2 digits of sqrt(2).

Does it have an analytic continuation into the critical strip?

Assuming so, can anything be said about the locations of its poles in this region? Are there any? Are they all on the critical line?

What about pi and e and log(2)?

Are all of these sequences "random" in the same sense as the Liouville and Moebius functions?

$$F\\,(s) = 1/1^s + 0/2^s + 1/3^s + 1/4^s + 0/5^s + 1/6^s + 0/7^s + 1/8^s + ... $$

The coefficients of this Dirichlet series are the base-2 digits of $\sqrt2$.

Does it have an analytic continuation into the critical strip?

Assuming so, can anything be said about the locations of its poles in this region? Are there any? Are they all on the critical line?

What about $\pi$ and $e$ and $\log 2$?

Are all of these sequences "random" in the same sense as the Liouville and Moebius functions?

F(s) = 1/1^s + 0/2^s + 1/3^s + 1/4^s + 0/5^s + 1/6^s + 0/7^s + 1/8^s + ...

The coefficients of this Dirichlet series are the base-2 digits of sqrt(2).

Does it have an analytic continuation into the critical strip?

Assuming so, can anything be said about the locations of its poles in this region? Are there any? Are they all on the critical line?

What about pi and e and log(2)?

F(s) = 1/1^s + 0/2^s + 1/3^s + 1/4^s + 0/5^s + 1/6^s + 0/7^s + 1/8^s + ...

The coefficients of this Dirichlet series are the base-2 digits of sqrt(2).

Does it have an analytic continuation into the critical strip?

Assuming so, can anything be said about the locations of its poles in this region? Are there any? Are they all on the critical line?

What about pi and e and log(2)?

Are all of these sequences "random" in the same sense as the Liouville and Moebius functions?