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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Faster computation of the first factor of the class number of $\textbf {Q}(\zeta _ p)$
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by Vijay Jha PDF
Math. Comp. 64 (1995), 1705-1710 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1705-1710
  • MSC: Primary 11R18; Secondary 11R29, 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1277768-4
  • MathSciNet review: 1277768