User:Hillgentleman/quasi-abelian function

多複變函數中，擬阿貝爾函數(quasi-abelian function)係種「退化」嘅阿貝爾函數(en:abelian function)。

More precisely, a quasi-abelian function is

• a function $f:\mathbb {C} ^{n}\longrightarrow \mathbb {C} ^{m}$ with
• coordinate system $z_{1},z_{2},...,z_{n}$
• positive integers p,q,r: p+q+r=n
• vectors $v_{1},v_{2},...,v_{2r}$

such that

• f is a rational function in each of the variables $z_{p+q+1},...,z_{n}$ and $e^{z_{p+1}},......,e^{z_{p+q}}$
• f is periodic in each vector $v_{1},v_{2},...,v_{2r}$
• the last r co-ordinate components of the vectors $v_{1},v_{2},...,v_{2r}$ are linearly independent over $\mathbb {R}$

...

參攷

• Etingof/Schiffmann, "Lectures on Quantum groups", p.63