Class numbers of cyclic 2-extensions and Gross conjecture over ℚ

Yi Ouyang; Hang Xue

doi:10.1007/s11425-010-4070-z

Class numbers of cyclic 2-extensions and Gross conjecture over ℚ

Yi Ouyang
, Hang Xue

Research output: Contribution to journal › Article › peer-review

Abstract

The Gross conjecture over ℚ was first claimed by Aoki in 1991. However, the original proof contains too many mistakes and false claims to be considered as a serious proof. This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki. We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of ℚ.

Original language	English (US)
Pages (from-to)	2447-2462
Number of pages	16
Journal	Science China Mathematics
Volume	53
Issue number	9
DOIs	https://doi.org/10.1007/s11425-010-4070-z
State	Published - 2010
Externally published	Yes

Keywords

Gross conjecture
class number
cyclic 2-extension

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-010-4070-z

Cite this

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abstract = "The Gross conjecture over ℚ was first claimed by Aoki in 1991. However, the original proof contains too many mistakes and false claims to be considered as a serious proof. This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki. We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of ℚ.",

keywords = "Gross conjecture, class number, cyclic 2-extension",

author = "Yi Ouyang and Hang Xue",

note = "Funding Information: Acknowledgements Research partially supported by National Natural Science Foundation of China (Grant No. 10871183) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200803580047).",

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PY - 2010

Y1 - 2010

N2 - The Gross conjecture over ℚ was first claimed by Aoki in 1991. However, the original proof contains too many mistakes and false claims to be considered as a serious proof. This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki. We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of ℚ.

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KW - Gross conjecture

KW - class number

KW - cyclic 2-extension

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Class numbers of cyclic 2-extensions and Gross conjecture over ℚ

Abstract

Keywords

ASJC Scopus subject areas

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