论文标题
雅各比衍生物公式的新概括
New generalisation of Jacobi's derivative formula
论文作者
论文摘要
获得了新的theta关系。它们遵循一般的Thomae公式，这是一个新的结果，给出了theta衍生物的表达（theta函数的最低非变化衍生物的零值，其分支点具有奇异的半期特性），以及分支点的周期矩阵的表达。新的theta关系包含（i）在一阶的矢量空间上的线性关系，这些属性是在梯度中排列的，（ii）二阶theta衍生物与梯度向量空间上的二阶theta衍生物与对称双线性形式之间的关系，（iii）在theta衍生物和对称阶层之间的三个阶三阶三个阶层之间的关系，以较高的梯度形成梯度的空间，（ever）在梯度上的渐变空间（以及（衍生物。它展示了如何从获得的关系中得出的肖特基身份（在过椭圆形的情况下）。
A stream of new theta relations is obtained. They follow from the general Thomae formula, which is a new result giving expressions for theta derivatives (the zero values of the lowest non-vanishing derivatives of theta functions with singular half-period characteristics) in terms of branch points and the period matrix of a hyperelliptic Riemann surface. The new theta relations contain (i) linear relations on the vector space of first order theta derivatives which are arranged in gradients, (ii) relations between second order theta derivatives and symmetric bilinear forms on the vector space of the gradients, (iii) relations between third order theta derivatives and symmetric trilinear forms on the vector space of the gradients, and (iv) a conjecture regarding higher order theta derivatives. It is shown how the Schottky identity (in the hyperelliptic case) is derived from the obtained relations.
