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    Investigations of Highly Irregular Primes and Associated Ray Class Fields

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    Stern_umd_0117E_15723.pdf (534.1Kb)
    No. of downloads: 284

    Date
    2014
    Author
    Stern, Morgan Benjamin
    Advisor
    Washington, Lawrence
    DRUM DOI
    https://doi.org/10.13016/M28S4K
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    Abstract
    We investigate properties of the class number of certain ray class fields of prime conductor lying above imaginary quadratic fields. While most previous work in this area restricted to the case of imaginary quadratic fields of class number 1, we deal almost exclusively with class number 2. Our main results include finding 5 counterexamples to a generalization of the famous conjecture of Vandiver that the class number of the pth real cyclotomic field is never divisible by p. We give these counterexamples the name highly irregular primes due to the fact that any counterexample of classical Vandiver is an irregular prime. In addition we explore whether several consequences of Vandiver's conjecture still hold for these highly irregular primes, including the cyclicity of certain class groups.
    URI
    http://hdl.handle.net/1903/16321
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    DRUM is brought to you by the University of Maryland Libraries
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