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

Yi Ouyang, Hang Xue

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)2447-2462
Number of pages16
JournalScience China Mathematics
Volume53
Issue number9
DOIs
StatePublished - 2010
Externally publishedYes

Keywords

  • class number
  • cyclic 2-extension
  • Gross conjecture

ASJC Scopus subject areas

  • Mathematics(all)

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