DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS IN GENUS(11)
发布时间：2021-06-05
Let #(u) and #(u) be the usual functions in the theory of elliptic functions. The following two formulae were found in the nineteenth-century. First one is
HYPERELLIPTICFUNCTIONSINGENUSTHREE11
Definition-Proposition2.13.Letnbeapositiveinteger.Ifu∈κ 1ι(C),thenσ(nu)ψn(u):=
σ2(u)σ2(v)22
Proof.IfweregardutobeavariableonC3,thefunction
u→σ(u+v)σ(u v) 1= 1 x(u) .x(v)
333
33
2(u v)
( u(3)3+···)2σ2(v)2= 1
