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dc.contributor.author楊一帆en_US
dc.contributor.authorYang Yifanen_US
dc.date.accessioned2014-12-13T10:41:38Z-
dc.date.available2014-12-13T10:41:38Z-
dc.date.issued2012en_US
dc.identifier.govdocNSC99-2115-M009-011-MY3zh_TW
dc.identifier.urihttp://hdl.handle.net/11536/98610-
dc.identifier.urihttps://www.grb.gov.tw/search/planDetail?id=2391310&docId=380298en_US
dc.description.abstract在本計畫中,我們將研究數個有關模形式的問題。包含 1. 分割數函數及其推廣的同餘性質, 2. 權為整數的模形式及權為半整數的模形式間的志村對應, 3. Hecke算子在Atkin-Lehner特徵子空間的trace公式及其應用, 4. 四元數的theta函數與模形式的關聯, 5. 四元數的theta函數的線性關係與橢圓曲線的算術性質的關聯。zh_TW
dc.description.abstractIn this research project, we will study several problems related to the theory of modular forms, including 1. Congruences of the partition function and its generalization, 2. Shimura correspondence between certain modular forms of half-integral weights and modular forms of integral weights. 3. Trace formulas for Hecke operators on Atkin-Lehner eigensubspaces of cusp forms. 4. Theta series attached to quaternion orders over Q and their relations to modular forms. 5. Linear dependences among theta series attached to quaternion orders over Q and their relations to arithmetic properties of elliptic curves over Q.en_US
dc.description.sponsorship行政院國家科學委員會zh_TW
dc.language.isozh_TWen_US
dc.title分割數函數, 志村對應, 四元theta函數及 L-函數的特殊值zh_TW
dc.titlePartition Function, Shimura Correspondence, Quaternary Theta Series, and Special Values of L-Functionsen_US
dc.typePlanen_US
dc.contributor.department國立交通大學應用數學系(所)zh_TW
Appears in Collections:Research Plans