ANOTHER LOOK AT GROSS-STARK UNITS OVER THE NUMBER FIELD Q
SCIE
SCOPUS
- Title
- ANOTHER LOOK AT GROSS-STARK UNITS OVER THE NUMBER FIELD Q
- Authors
- Park, J
- Date Issued
- 2011-08
- Publisher
- World Scientific
- Abstract
- We provide another description of the Gross-Stark units over the rational field Q (studied in [B. Gross, p-Adic L-series at s = 0, J. Fac. Sci. Univ. Tokyo 28(3) (1981) 979-994]) which is essentially a Gauss sum, using a p-adic multiplicative integral of the p-adic Kubota-Leopoldt distribution, and give a simplified proof of the Ferrero-Greenberg theorem (see [B. Ferrero and R. Greenberg, On the behavior of p-adic L-functions at s = 0, Invent. Math. 50(1) (1978/79) 91-102]) for p-adic Hurwitz zeta functions. This is a precise analog for Q of Darmon-Dasgupta's work on elliptic units for real quadratic fields (see [H. Darmon and S. Dasgupta, Elliptic units for real quadratic fields, Ann. of Math. (2) 163(1) (2006) 301-346]).
- Keywords
- Gross-Stark conjecture; p-adic Gross-Stark units; p-adic multiplicative integrals; Ferrero-Greenberg theorem; REAL QUADRATIC FIELDS; ELLIPTIC UNITS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/25125
- DOI
- 10.1142/S1793042111004150
- ISSN
- 1793-0421
- Article Type
- Article
- Citation
- INTERNATIONAL JOURNAL OF NUMBER THEORY, vol. 7, no. 5, page. 1379 - 1393, 2011-08
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