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Arithmetic properties of j-function

Das, Jishu (2018) Arithmetic properties of j-function. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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    Abstract

    Modular forms play an significant role in number theory. They also appear in areas like algebraic topology and string theory. The j-function is a very special function in the theory of modular forms. In particular, modular forms of weight zero are polynomials in j-function which we prove in this thesis. The main goal of this thesis, however will be to explore some important properties of j-function, define modular functions for Γ₀ (m) and give a classification of it. Then we define the modular equation, explore some of its properties and use these properties to show that j(Ok)is an algebraic integer where Ok is the ring of integers of Q(√-n)for n being a square free natural number.

    Item Type: Thesis (Masters)
    Additional Information: Supervisor: Dr. Swarnendu Datta
    Uncontrolled Keywords: Arithmetic Properties; j-function; Modular Forms
    Subjects: Q Science > QA Mathematics
    Divisions: Department of Mathematics and Statistics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 11 Dec 2018 11:10
    Last Modified: 11 Dec 2018 11:11
    URI: http://eprints.iiserkol.ac.in/id/eprint/759

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