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StickelbergerClassNumber.pdf (337.67 KB)
ETD Abstract Container
Abstract Header
The Stickelberger Ideal and the Cyclotomic Class Number
Author Info
Bond, Jacob
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1366371004
Abstract Details
Year and Degree
2013, Master of Science, Ohio State University, Mathematics.
Abstract
The ideal class group is an important object in the study of algebraic number fields, as is the associated class number. In cyclotomic fields in particular, the class number decomposes into two factors. While the second factor is difficult to determine due to the need for a basis of the group of units, the first factor is given by a surprisingly simple formula. In terms of the structure of the ideal class group, Stickelberger's theorem gives an important result. The theorem provides explicit annihilators of the ideal class group, from which the Stickelberger ideal arises. In this work, the analytic class number formula is derived and related to the minus part of the index of the Stickelberger ideal in the integral group ring over the Galois group.
Committee
Warren Sinnott (Advisor)
James Cogdell (Committee Member)
Subject Headings
Mathematics
Keywords
Stickelberger
;
class number
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Citations
Bond, J. (2013).
The Stickelberger Ideal and the Cyclotomic Class Number
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366371004
APA Style (7th edition)
Bond, Jacob.
The Stickelberger Ideal and the Cyclotomic Class Number.
2013. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1366371004.
MLA Style (8th edition)
Bond, Jacob. "The Stickelberger Ideal and the Cyclotomic Class Number." Master's thesis, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366371004
Chicago Manual of Style (17th edition)
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Document number:
osu1366371004
Download Count:
906
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.