Safe convergence of Chebyshev-like method.
We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.
We shall investigate the properties of solutions of second order linear difference equations defined over a discrete Hardy field via canonical valuations.
Abhyankar proved that every field of finite transcendence degree over or over a finite field is a homomorphic image of a subring of the ring of polynomials (for some depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .