Form Class Groups Isomorphic to the Galois Groups over Ring Class Fields
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let K be an imaginary quadratic field and O be an order in K. Let HO be the ring class field of O. Furthermore, for a positive integer N, let KO,N be the ray class field modulo NO of O. When the discriminant of O is different from −3 and −4, we construct an extended form class group which is isomorphic to the Galois group Gal(KO,N /HO ) and describe its Galois action on KO,N in a concrete way.
Abstract
Let K be an imaginary quadratic field and O be an order in K. Let HO be the ring class field of O. Furthermore, for a positive integer N, let KO,N be the ray class field modulo NO of O. When the discriminant of O is different from −3 and −4, we construct an extended form class group which is isomorphic to the Galois group Gal(KO,N /HO ) and describe its Galois action on KO,N in a concrete way.
참고문헌 (7)
- B. Cho, "Primes of the form x2 + ny2 with conditions x ≡ 1 mod N, y ≡ 0 mod N", J. Number Theory, 130(4), pp.852~861 (2010)
- D. A. Cox, "Primes of the Form x2 + ny2 : Fermat, Class field theory, and Complex Multiplication. Pure and Applied Mathematics" (2013), John Wiley & Sons, Inc
- I. S. Eum, "Binary quadratic forms and ray class groups", Proc. Roy. Soc. Edinburgh Sect. A, 150(2), pp.695~720 (2020)
- "Arithmetic of orders in imaginary quadratic fields"[URL]
- S. Lang, "Algebra" (2002), Springer-Verlag
- S. Lang, "Elliptic Functions" (1987), Spinger-Verlag
- P. Stevenhagen, "Class field theory—its centenary and prospect", pp.161~176 (2001), Math. Soc. Japan