Powerful Necessary Conditions for Class Number Problems | Zendy

Louboutin Stéphane | Zendy

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Powerful Necessary Conditions for Class Number Problems

Author(s) -

Louboutin Stéphane

Publication year - 1997

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19971830111

Subject(s) - mathematics , quartic function , exponent , ideal class group , class (philosophy) , ideal (ethics) , algebraic number field , class field theory , quadratic equation , computation , class number , field (mathematics) , pure mathematics , discrete mathematics , geometry , algorithm , philosophy , linguistics , epistemology , artificial intelligence , computer science

We give a necessary condition for the ideal class group of a CM‐field to be of exponent at most two. This condition enables us to drastically reduce the amount of relative class number computation for determination of the CM ‐ fields of some types (e. g. the imaginary cyclic non ‐quadratic number fields of 2 ‐ power degrees) whose ideal class groups are of exponents at most two. We also give a necessary condition for some quartic non ‐ CM ‐ fields to have class number one.

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