Analytic Class Number Formula

Roy, Soumyajit (2025) Analytic Class Number Formula. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Soumyajit Roy (23MP031)) 23MP031_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (752kB)

Abstract

This thesis assumes a basic understanding of the definitions and properties of the ring of integers in a number field, as well as fundamental concepts from complex analysis, such as the analyticity of functions. In particular, we assume familiarity with the finiteness of the class group of a number field and the key ideas involved in its proof. The primary goal of this thesis is to present a proof of the class number formula, which expresses the class number of a number field in terms of its Dedekind Zeta Function. This formula was originally proved by Dedekind for general number fields.

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