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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Greenberg’s conjecture for real quadratic fields and the cyclotomic $\mathbb {Z}_2$-extensions
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by Lorenzo Pagani HTML | PDF
Math. Comp. 91 (2022), 1437-1467 Request permission


Let $\mathcal {A}_n$ be the $2$-part of the ideal class group of the $n$-th layer of the cyclotomic $\mathbb {Z}_2$-extension of a real quadratic number field $F$. The cardinality of $\mathcal {A}_n$ is related to the index of cyclotomic units in the full group of units. We present a method to study the latter index. As an application we show that the sequence of the $\mathcal {A}_n$’s stabilizes for the real fields $F=\mathbb {Q}(\sqrt {f})$ for any integer $0<f<10000$. Equivalently Greenberg’s conjecture holds for those fields.
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Additional Information
  • Lorenzo Pagani
  • Affiliation: Dipartimento di matematica, università di Roma “La Sapienza”, piazzale Aldo Moro 5, 00185 Roma, Italy
  • Email:
  • Received by editor(s): March 23, 2021
  • Received by editor(s) in revised form: August 8, 2021, September 28, 2021, and October 17, 2021
  • Published electronically: December 30, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 1437-1467
  • MSC (2020): Primary 11R29, 11Y40; Secondary 11R23
  • DOI:
  • MathSciNet review: 4405501