Computation of relative class numbers of imaginary cyclic fields of 2-power degrees
In this abridged version of [Lou], we outline an efficient technique for computing relative class numbers of imaginary abelian fields. It enables us to compute relative class numbers of imaginary cyclic fields of degrees 32 and conductors greater than 1013, or of degrees 4 and conductors greater than 1015. Our major innovation is a technique for computing numerically root numbers appearing in some functional equations.
Mathematics Subject Classification11R20 11R29 11Y40 11M20 11R42
KeywordsImaginary abelian number field relative class number
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