標題: | Differential equations satisfied by modular forms and K3 surfaces |
作者: | Yang, Yifan Yui, Noriko 應用數學系 Department of Applied Mathematics |
公開日期: | 1-六月-2007 |
摘要: | We study differential equations satisfied by modular forms of two variables associated to Gamma(1) x Gamma(2), where Gamma(i) (i = 1, 2) are genus zero subgroups of SL2(R) commensurable with SL2(Z), e.g., Gamma(0)(N) or Gamma(0)(N)* for some N. In some examples, these differential equations are realized as the Picard-Fuchs differential equations of families of K3 surfaces with large Picard numbers, e.g., 19,18,17,16. Our method rediscovers some of the Lian-Yau examples of "modular relations" involving power series solutions to the second and the third order differential equations of Fuchsian type in [14], [15]. |
URI: | http://hdl.handle.net/11536/10716 |
ISSN: | 0019-2082 |
期刊: | ILLINOIS JOURNAL OF MATHEMATICS |
Volume: | 51 |
Issue: | 2 |
起始頁: | 667 |
結束頁: | 696 |
顯示於類別: | 期刊論文 |