UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Avila Artavia, Josue David

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    CYCLOTOMIC Z2-EXTENSION OF REAL QUADRATIC FIELDS WITH CYCLIC IWASAWA MODULE
    (2024) Avila Artavia, Josue David; Ramachandran, Niranjan; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    For a number field K and a prime p, let K∞ denote the cyclotomic Zp-extension of K, andAn denote the p-primary part of the class group of its n-th layer Kn. Greenberg conjectured that for a totally real field, the order of An becomes constant for sufficiently large n. Motivated by the work of Mouhib and Movahhedi, we focus on the case where p = 2 and K is a real quadratic field such that the Iwasawa module X∞ = lim←An is cyclic. They determined all such fields and proved that Greenberg’s conjecture holds for some cases. In this dissertation, we provide new examples of infinite families of real quadratic fields satisfying Greenberg’s conjecture which were not covered completely in the work of Mouhib and Movahhedi. To achieve this, we use the theory of binary quadratic forms and biquadratic extensions to determine a fundamental system of units and the class number of the first few layers of the cyclotomic Z2-extension. Additionally, in certain cases, we can determine the size of the module X∞ and the level of the cyclotomic tower where the size of An becomes constant.