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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PDF (MS Dissertation of Manami Roy)
Manami_Roy-11IP02-MSThesis.pdf - Submitted Version Restricted to Repository staff only Download (330kB) |
Official URL: http://www.iiserkol.ac.in
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 03:48 |
| Last Modified: | 12 Nov 2014 04:33 |
| URI: | http://eprints.iiserkol.ac.in/id/eprint/48 |
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