Full metadata record
DC FieldValueLanguage
dc.contributor.author林易萱en_US
dc.contributor.authorLin, Yi-Hsuanen_US
dc.contributor.author楊一帆en_US
dc.contributor.authorYang, Yifanen_US
dc.date.accessioned2014-12-12T01:49:36Z-
dc.date.available2014-12-12T01:49:36Z-
dc.date.issued2010en_US
dc.identifier.urihttp://140.113.39.130/cdrfb3/record/nctu/#GT079822517en_US
dc.identifier.urihttp://hdl.handle.net/11536/47517-
dc.description.abstract 眾所周知的,費馬曲線 x^n+y^n=1 是一個與特殊線性群SL_2(Z)的有限指數子群Γ_n相關聯的模曲線,當n不等於1, 2, 4, 8時, Γ_n是一個非同餘子群。現在令費馬曲線的虧格為g,scholl的定理告訴我們,Γ_n上權為2的尖點型式與由此曲線相關聯的Tate模所建構出的2g維l進數伽羅瓦表現會滿足Atkin and Swinnerton-Dyer同餘。   在這篇論文中,我們將會分解伽羅瓦表現,然後給一個更加精確的Atkin and Swinnerton-Dyer同餘。我們將會解決n=6的情況。zh_TW
dc.description.abstractIt is known that each Fermat curve x^n+y^n=1 is the modular curve associated to some subgroup Γ_n of SL_2(Z) of finite index. Moreover if n≠1,2,4,8 then Γ_n is a noncongruence subgroup. Let g be the genus of the Fermat curve, by Scholl’s theorem, cuspforms of weight 2 on Γ_n, together with the 2g-dimensional l-adic Galois representations coming from the Tate module associate this curve, satisfy the Atkin and Swinnerton-Dyer congruence. In this thesis, we decompose this Galois representation and give a more precise Atkin and Swinnerton-Dyer congruence. The case n=6 will be completely worked out.en_US
dc.language.isoen_USen_US
dc.subject模形式zh_TW
dc.subject費馬曲線zh_TW
dc.subjectASD同餘zh_TW
dc.subjectModular formen_US
dc.subjectFermat curveen_US
dc.subjectASD congruenceen_US
dc.title非同餘子群的模型式的同餘性質zh_TW
dc.titleAtkin and Swinnerton-Dyer congruences associated to Fermat curvesen_US
dc.typeThesisen_US
dc.contributor.department應用數學系所zh_TW
Appears in Collections:Thesis


Files in This Item:

  1. 251701.pdf

If it is a zip file, please download the file and unzip it, then open index.html in a browser to view the full text content.