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The Ramanujan's Conjectures and L-functions Corresponding to Cusp Forms

Roy, Manami (2013) The Ramanujan's Conjectures and L-functions Corresponding to Cusp Forms. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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    Abstract

    This thesis is focused on the study of modular forms and Hecke operators. In particular, we mainly concentrate on Ramanujan's conjectures, a collection of three conjectures on the pai (π)-function, and the L-functions corresponding to cusp forms. In the context of Ramanujan's conjectures, proofs are provided for the first two and a weaker version of the third one. Furthermore, we also study various properties of the L-functions corresponding to the cusp forms on SL2(Z), deriving the functional equation and analytic continuation in the process.

    Item Type: Thesis (Masters)
    Additional Information: Supervisor: Dr. Saugata Bandyopadhyay
    Uncontrolled Keywords: Ramanujan's Conjectures; L-functions; Cusp Forms; Modular Forms; Hecke Operators
    Subjects: Q Science > QA Mathematics
    Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
    Depositing User: IISER Kolkata Librarian
    Date Deposited: 06 May 2013 09:18
    Last Modified: 12 Nov 2014 10:03
    URI: http://eprints.iiserkol.ac.in/id/eprint/48

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