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Simple zero property of some holomorphic functions on the moduli space of tori
- Publication Year :
- 2017
-
Abstract
- We prove that some holomorphic functions on the moduli space of tori have only simple zeros. Instead of computing the derivative with respect to the moduli parameter $\tau$, we introduce a conceptual proof by applying Painlev\'{e} VI\ equation. As an application of this simple zero property, we obtain the smoothness of all the degeneracy curves of trivial critical points for some multiple Green function.<br />Comment: 20 pages, 1 figure
- Subjects :
- Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1703.05521
- Document Type :
- Working Paper