Real and complex behaviour of the base change function (was: The "cheta" function)

[jaydfox]

But doesnt this mean that the singularities that come close to the real axis somehow accumulate around 0?

At least the minimum of the spiral will be around 0. I think I could even calculate bounds on the real axis around 0 in which the minimum of every such spiral has to live.

Don't take this wrong, as I mean no offense, but I'm not really sure what you're getting at. I'm not sure what you mean by singularities accumulating around 0. Indeed, for any given n, they accumulate around the real line, even for n as low as 5, and the accumulation gets denser as we move up the real line, to larger and larger real part.

But perhaps we are speaking of two different things?