Abstract. We characterize meromorphic function fields closed by partial derivatives in $n$ variables.

DOI: 10.14232/actasm-018-530-7

AMS Subject Classification (1991): 32A20; 32W50

Keyword(s): algebraic addition theorem, degenerate Abelian functions, Briot--Bouquet type partial differential equations

Received March 22, 2018 and in final form March 6, 2019. (Registered under 30/2018.)