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Analytic Class Number Formula

Maisnam, Sanjeet (2018) Analytic Class Number Formula. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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    Abstract

    Let K be a number field and Ok be its number ring The number of ideals of Ok with norm bounded by a positive real number t can be approximated by µt, where µ is a constant involving many invariants of Ok. If we consider the Dedekind zeta function ζk(s) of K, it has a meromorphic continuation to the half plane defined by Re(s)> 1- 1/[K:Q] which has only a simple pole at s = 1 with residue µ. The class number formula can be obtained from µ. In this manner, the class number relates many invariants of OK to a special value of ζk(s), which is the residue of ζk(s) at s = 1.

    Item Type: Thesis (Masters)
    Additional Information: Supervisor: Dr. Swarnendu Datta
    Uncontrolled Keywords: Algebraic Number Theory; Analytic Class Number; Number Ring
    Subjects: Q Science > QA Mathematics
    Divisions: Department of Mathematics and Statistics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 13 Dec 2018 10:34
    Last Modified: 13 Dec 2018 10:35
    URI: http://eprints.iiserkol.ac.in/id/eprint/772

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