P - Adic L Functions

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Sanjari, Ali | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40558 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Shahshahani, Siavash
Abstract:
Using interpolation and starting with Bernoulli numbers, posed by Leopold and Kubota, the aspect of adic function was constructed as adic analogues of the Dirichlet functions.Studing Galois module theory of ideal class group and his favorite structure extensions and modules related to them,Iwasawa found a new method for constructing adic functions by using Stickelberger’s elements.These results wich established by Iwasawa are known as Iwasawa Theory and they have many application in Algebriac Number Theory. Iwasawa’s most remarkable disconvry is the facet that at least in some important cases, there is a similar deep algebraic and analytic dichotomy in arithmetic of extensions. A precise formulation of this dichotomy is often called “the main conjecture”. In this thesis we try to try to explain a selection of these investingations around adic functions and Iwasawa Theropry with direction to their application in Algebraic Number Theory and especially in finding a formula for class number.
Keywords:
Cyclotomic Field ; P-Adic Field ; L-Function

No TOC