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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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 03:48
Last Modified: 12 Nov 2014 04:33

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