CHARACTERIZATION OF A CYCLIC GROUP RING IN TERMS OF CHARACTER VALUES

DOI QR코드

DOI QR Code

Lee, Joongul

  • 투고 : 2014.08.20
  • 발행 : 2015.01.31

초록

Let G be a cyclic group of prime power order. There is a natural embedding of $\mathbb{Z}[G]$ into a product of rings of integers of cyclotomic fields. In this paper the image of the embedding is determined, and we also compute the index of the image.

키워드

group rings

참고문헌

  1. D. Burns, Congruences between derivatives of abelian L-functions at s = 0, Invent. Math. 169 (2007), no. 3, 451-499. https://doi.org/10.1007/s00222-007-0052-3
  2. B. H. Gross, On the values of abelian L-functions at s = 0, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 35 (1988), no. 1, 177-197.
  3. J. Lee, Congruences of L-values for cyclic extensions, Honam Math. J. 32 (2010), no. 4, 791-795. https://doi.org/10.5831/HMJ.2010.32.4.791
  4. B. Mazur and J. Tate, Refined conjectures of the "Birch and Swinnerton-Dyer type", Duke Math. J. 54 (1987), no. 2, 711-750. https://doi.org/10.1215/S0012-7094-87-05431-7
  5. K. Rubin, A Stark conjecture "over Z" for abelian L-functions with multiple zeros, Ann. Inst. Fourier (Grenoble) 46 (1996), no. 1, 33-62. https://doi.org/10.5802/aif.1505

피인용 문헌

  1. 1. POWERS OF THE AUGMENTATION IDEAL OF A CYCLIC GROUP RING vol.37, pp.2, 2015, doi:10.4134/CKMS.2015.30.1.001

과제정보

연구 과제 주관 기관 : Hongik University