08Nov 2018
14:15 - 15:15

Gastvorlesung / Vortrag

Number Theory Seminar: David Masser (Univ. of Basel)

Solving polynomial-exponential equations.

Inspired by Schanuel's Conjecture, Boris Zilber has proposed a Nullstellensatz'' (also conjectural) asserting which sorts of polynomial-exponential equations in several variables have a complex solution. Last year Dale Brownawell and I published a proof in the situation which can be regarded as typical''. But it does not cover all situations for two variables, some of which involve simply stated problems in one variable like finding complex $z \neq 0$ with $e^z+e^{1/z}=1$. Recently Vincenzo Mantova and I have settled the general case of two variables. We describe our methods -- for example, to solve
$$e^z+e^{\root 9 \of {1-z^9}}=1$$
one approach uses theta functions on ${\bf C}^{28}$.

Veranstaltung übernehmen als iCal