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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.

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