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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Faster computation of the first factor of the class number of $\textbf {Q}(\zeta _ p)$

Author: Vijay Jha
Journal: Math. Comp. 64 (1995), 1705-1710
MSC: Primary 11R18; Secondary 11R29, 11Y40
MathSciNet review: 1277768
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Abstract: We describe two fast methods for computing the first factor of the class number of the cyclotomic field $\mathbb {Q}({\zeta _p})$ in $\mathcal {O}({p^2}{\log ^5}p)$ and $\mathcal {O}({p^2}\log p)$ steps of elementary arithmetic operations on the numbers of size p, respectively. The first is deterministic, while the second holds under the GRH. This is an improvement over the previous method of Lehmer and Masley, which has complexity $\mathcal {O}({p^{3.81}})$.

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Article copyright: © Copyright 1995 American Mathematical Society