Maisnam, Sanjeet (2018) Analytic Class Number Formula. Masters thesis, Indian Institute of Science Education and Research Kolkata.
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PDF (MS dissertation of Sanjeet Maisnam (13MS143))
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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 05:04 |
| Last Modified: | 13 Dec 2018 05:05 |
| URI: | http://eprints.iiserkol.ac.in/id/eprint/772 |
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