Abstract
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.
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References
B.C. Berndt and R.J. Evans. The determination of Gauss sums. Bull. Amer. Math. Soc. 5 (2) (1981), 107–129.
S. Louboutin. Computation of relative class numbers of imaginary abelian number fields. Experimental Math, to appear.
L.C. Washington. Introduction to Cyclotomic Fields. Grad.Texts Math. 83, Springer-Verlag (1982); Second Edition: 1997.
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© 1998 Springer-Verlag Berlin Heidelberg
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Louboutin, S. (1998). Computation of relative class numbers of imaginary cyclic fields of 2-power degrees. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054886
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DOI: https://doi.org/10.1007/BFb0054886
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