ON A GENERALIZATION OF WIRTINGER'S INTEGRAL

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概要

• 論文の詳細を見る

• W. Wirtinger, in 1902, introduced an integral representation for the Gauss hypergeometric function in terms of theta functions. We give a generalization of this integral representation. More concretely, we study a definite integral of a power product of theta functions which has zeros at N-torsion points (N is a natural number greater than one) on a one-dimensional complex torus. We show that this integral gives a solution of a system of Fuchsian differential equations on the modular curve of level N and determine the spectral types of the system at its regular singularities.

• 九州大学大学院数理学研究院の論文

著者

• Mano Toshiyuki

  Department Of Developmental Medicine (pediatrics) Osaka University Graduate School Of Medicine

• MANO Toshiyuki

  Department of Mathematical Sciences Faculty of Science University of the Ryukyus

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• ON A GENERALIZATION OF WIRTINGER'S INTEGRAL

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