Integral Evaluation on Three-sheeted Riemann Surface of Genus N of Type I
碩士 === 國立交通大學 === 應用數學系 === 89 === The integrals over a,b cycles on Riemann surface can solve some problems in differential Equations. We use algebraic and geometric method to construct three-sheeted Riemann surfaces of genus N such that a multi-valued function is single-valued and analyt...
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| Format: | Others |
| Language: | en_US |
| Published: |
2001
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| Online Access: | http://ndltd.ncl.edu.tw/handle/65807328629749867603 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系 === 89 === The integrals over a,b cycles on Riemann surface can solve some problems in differential Equations. We use algebraic and geometric method to construct three-sheeted Riemann surfaces of genus N such that a multi-valued function is single-valued and analytic on the Riemann surface. Then, by Cauchy integral theorem, we can find equivalent paths of a,b cycles such that the two integrals are equal. The equivalent path-integrals along cuts can be computed by "Mathematica" simply and correctly.
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