Jacobi导数公式的新推广
New generalisation of Jacobi's derivative formula
摘要：
一个新的theta关系流。这是一个新的结果，它给出了θ导数（具有奇异半周期特征的θ函数的最低非零导数的零值）关于超椭圆Riemann曲面的分支点和周期矩阵的表达式.新的θ关系包含（i）一阶θ导数在梯度向量空间上的线性关系，（ii）二阶θ导数与梯度向量空间上的对称双线性型的关系，（iii）三阶θ导数与梯度向量空间上的对称三线性型的关系，以及（iv）关于高阶θ导数的猜想。它示出了如何肖特基身份（在超椭圆的情况下）来自所获得的关系。
英文摘要：
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.
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