# On the integral \$ I_s = int_ {1} ^ { infty} ( pi (x) -Li (x)) x ^ {- s-1} dx \$

To define $$pi (x)$$ be the first count function and Li (x) the logarithmic integral. Let $$I_s$$ to be defined as above.

is $$I_s$$ known to be convergent for any real number $$s < 1$$ ?