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1998 Computation of relative class numbers of imaginary abelian number fields
Stéphane Louboutin
Experiment. Math. 7(4): 293-303 (1998).

Abstract

We develop an efficient technique for computing relative class numbers of imaginary abelian fields, efficient enough to enable us to easily compute relative class numbers of imaginary cyclic fields of degrees $32$ and conductors greater than $10^{13}$, or of degrees $4$ and conductors greater than $10^{15}$. Acccording to our extensive computation, all the $166204$ imaginary cyclic quartic fields of prime conductors $p$ less than $10^7$ have relative class numbers less than $p$/2. Our major innovation is a technique for computing numerically root numbers appearing in some functional equations.

Citation

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Stéphane Louboutin. "Computation of relative class numbers of imaginary abelian number fields." Experiment. Math. 7 (4) 293 - 303, 1998.

Information

Published: 1998
First available in Project Euclid: 14 March 2003

zbMATH: 0929.11065
MathSciNet: MR1678103

Subjects:
Primary: 11Y40
Secondary: 11M20, 11R20, 11R29

Rights: Copyright © 1998 A K Peters, Ltd.

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Vol.7 • No. 4 • 1998
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