In 'Cyclotomy and analytic geometry over F1', Manin proposes a version of the notion of `analytic function' over the 'field with one element $\mathbb F_1$'.
Question 1: can somebody explain or give an insight of what it is?
The logarithm is a basic analytic function. It seems natural to expect from any `good' theory of 'analytic functions' to have his own version of the logarithm.
Question 1: is there a version of the logarithm over $\mathbb F_1$? If yes, how it looks like?
Thanks in advance.