Some studies on the Shimura reciprocity law = Shimura 상호법칙에 관한 고찰

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 320
  • Download : 0
We mainly focus on the field $\mathfrak{F}$ of all modular functions of all level whose Fourier coefficients belong to cyclotomic fields. $Aut(\mathfrak{F})$ is isomorphic to the adelization of $GL_2(\mathbb{Q})$ modulo rational scalar matrices and the archimedean part. Then reciprocity law in the maximal abelian extension of an imaginary quadratic field is given as a certain commutativity of the action of the adeles with the specialization of the functions of $\mathfrak{F}$. In chapter 1, we briefly review some elementary facts about elliptic curves and adelizations. In chapter 2, we introduce the modular function field of level $N$. In chapter 3, we obtain a canonical exact sequence for a number field in idelic language. Further we state the main theorem of complex multiplication of elliptic curves and how to construct class fields using elliptic curves. In the last chapter, we discuss the structure of $Aut(\mathfrak{F})$ and the Shimura reciprocity law at the fixed points of $GL_2(\mathbb{Q})$ on $\mathfrak{H}$. We apply the Shimura reciprocity law to determine when the values of modular functions of higher level can be used to generate the Hilbert class field of an imaginary quadratic field.
Advisors
Koo, Ja-Kyungresearcher구자경researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2006
Identifier
255250/325007  / 020043292
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수학전공, 2006.2, [ iii, 36 p. ]

Keywords

adelization; Class field theory; modular function; 아델화; 유체; 보형함수

URI
http://hdl.handle.net/10203/42136
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=255250&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0