Maisnam, Sanjeet (2018) *Analytic Class Number Formula.* Masters thesis, Indian Institute of Science Education and Research Kolkata.

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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) |
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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 10:34 |

Last Modified: | 13 Dec 2018 10:35 |

URI: | http://eprints.iiserkol.ac.in/id/eprint/772 |

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