Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CHARACTERIZATION OF A CYCLIC GROUP RING IN TERMS OF CHARACTER VALUES

  • Lee, Joongul (Department of Mathematics Education Hongik University)
  • Received : 2014.08.20
  • Published : 2015.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  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

Cited by

  1. POWERS OF THE AUGMENTATION IDEAL OF A CYCLIC GROUP RING vol.37, pp.2, 2015, https://doi.org/10.5831/HMJ.2015.37.2.265