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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Yi Ouyang & Hang Xue

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  1. Yi Ouyang
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  2. Hang Xue
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Correspondence to Yi Ouyang.

Additional information

Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

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Ouyang, Y., Xue, H. Class numbers of cyclic 2-extensions and Gross conjecture over ℚ. Sci. China Math. 53, 2447–2462 (2010). https://doi.org/10.1007/s11425-010-4070-z

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  • DOI: https://doi.org/10.1007/s11425-010-4070-z

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