Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Riemann-Wirtinger integrals on the product of two one-dimensional complex tori

Yoshiaki Goto

Abstract

The Riemann-Wirtinger integral is an analogue of the hypergeometric integral defined on a one-dimensional complex torus. As a generalization, we define the Riemann-Wirtinger integral on the product of two one-dimensional complex tori. We study the structure of the twisted cohomology group associated with the Riemann-Wirtinger integral and derive a system of differential equations satisfied by this integral.

Riemann-Wirtinger integrals on the product of two one-dimensional complex tori

Abstract

The Riemann-Wirtinger integral is an analogue of the hypergeometric integral defined on a one-dimensional complex torus. As a generalization, we define the Riemann-Wirtinger integral on the product of two one-dimensional complex tori. We study the structure of the twisted cohomology group associated with the Riemann-Wirtinger integral and derive a system of differential equations satisfied by this integral.
Paper Structure (16 sections, 8 theorems, 51 equations)

This paper contains 16 sections, 8 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Twisted cohomology group
  4. Settings
  5. Twisted cohomology group
  6. Differential forms
  7. Differential equations
  8. Main theorem
  9. Computing $\nabla _{1p}(\psi_{ij})$, $\nabla _{1p}(\psi_{i \pm})$, $\nabla _{1p}(\psi_{\pm j})$ ($i\neq p$)
  10. Computing $\nabla _{1p}(\psi_{+-,m})$
  11. Computing $\nabla _{1p}(\psi_{pj})$
  12. Computing $\nabla _{1p}(\psi_{p\pm})$
  13. Computing $\nabla _{2q}$
  14. Some formulas
  15. Basic formulas
  16. ...and 1 more sections

Key Result

Proposition 3.3

Theorems & Definitions (15)

  • Remark 3.2
  • Proposition 3.3
  • proof
  • Theorem 3.4
  • proof
  • Remark 4.1
  • Theorem 4.2
  • Lemma A.1
  • proof
  • Lemma A.2
  • ...and 5 more