The Hasse norm theorem mod squares

David B. Leep, A. R. Wadsworth

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


For a Galois extension K F of global fields, char F≠2, it is known that the Hasse norm theorem mod squares is equivalent to the existence of a local-global principle for the transfer ideal JK/F of quadratic forms. When Gal(K/F)=(Z/2Z)k, the Hasse norm theorem mod squares holds although the usual Hasse norm theorem may fail. In this paper we analyze the case when Gal(K/F)=Z/2Z⊕Z/2kZ, k≥2. In particular, the Hasse norm theorem mod squares holds if and only if the Hasse norm theorem holds (Theorem I). A corollary shows that if a square in F is a local norm from K, then it is a global norm from K (Theorem II).

Original languageEnglish
Pages (from-to)337-348
Number of pages12
JournalJournal of Number Theory
Issue number3
StatePublished - Nov 1992

Bibliographical note

Funding Information:
l Supported in part by the NSF.

ASJC Scopus subject areas

  • Algebra and Number Theory


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