### CHARACTERIZATION OF A CYCLIC GROUP RING IN TERMS OF CHARACTER VALUES

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Lee, Joongul

• 투고 : 2014.08.20
• 발행 : 2015.01.31
• 6 4

#### 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.

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