open problems survey

[Catullus]

Conjecture:

The standard extension of exponentiation is the only extension of exponentiation, such that a to the power of x is totally monotonic, For all real a between one and zero non inclusive, and for all real a.

OHHHHHH CATULLUS!!!

This is a good one.

I'd suggest an old thread by me on MathOverflow, but it's lost in all the overflow.

I think that this is the thread.

[Catullus]

Conjecture:

\(\forall a,b\in\Bbb N-1\:\lim_{t\to\infty}g_a(b\uparrow\uparrow\lfloor t\rfloor)\in\overline{\Bbb Q}\iff b\div a\in\Bbb N\), where \(g_a\) denotes the a-ary van der Corput sequence.