Entire functions sharing simple aa-points with their first derivative

We show that if a complex entire function $f$ and its derivative $f'$ share their simple zeroes and their simple $a$-points for some nonzero constant $a$, then $f\equiv f'$. We also discuss how far these conditions can be relaxed or generalized. Finally, we determine all entire functions $f$ such that for 3 distinct complex numbers $a_1,a_2,a_3$ every simple $a_j$-point of $f$ is an $a_j$-point of $f'$.Comment: v3: 11 pages, corrected a typo in Theorem 2', updated address; refereed version, but note that the journal version carries my old address and has a finer division into sections and a different numbering of the theorem

On Elliptic Curves over Function Fields of Characteristic Two

AbstractUsing Drinfeld modular curves we determine the places of supersingular reduction of elliptic curves over F2r(T) with certain conductors. This enables us to classify and describe explicitly all elliptic curves over F2r(T) having a conductor of degree 4. Our results also imply that extremal elliptic surfaces over the algebraic closure of F2 are unirational