The Riemann–Wirtinger Integral and Monodromy-Preserving Deformation on Elliptic Curves
The Riemann–Wirtinger Integral and Monodromy-Preserving Deformation on Elliptic Curves
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椭圆曲线上的黎曼-维廷格积分和保单性变形
DOI：
10.1093/imrn/rnn110
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发表时间：
2010
影响因子：
1
通讯作者：
Toshiyuki Mano
中科院分区：
文献类型：
--
作者：
Toshiyuki Mano
我们研究由定积分定义的函数，其被积函数是指数函数和theta函数的幂乘积，我们称之为Riemann-Wirtinger积分。我们表明，这些功能描述特殊的解决方案的monodromy-preserving变形的Fuchsian微分方程的椭圆曲线。此外，我们建立了一些基本性质的Riemann-Wirtinger积分：差分方程的位移参数（邻接关系），计算monodromy矩阵，和描述的模变换的性质。
We study the functions defined by definite integrals whose integrands are power products of an exponential function and theta functions, which we call the Riemann-Wirtinger integrals. We show that those functions describe special solutions to the monodromy-preserving deformation of Fuchsian differential equations on elliptic curves. In addition, we establish some basic properties of the Riemann-Wirtinger integral: difference equations for the shifts of parameters (contiguity relations), computations of monodromy matrices, and description of modular transformation properties.