Abstract/Details

Asymptotically good towers of global function fields and bounds for the Ihara function


2009 2009

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Abstract (summary)

This is a thesis in Algebraic Number Theory, concerned with the study of bounds for the Ihara function, an asymptotic measure comparing the number of rational places of a global function field with the genus of that field. The exact behavior of this function is unknown; however, some bounds on its values are known. There is a sharp upper bound, proven by Drinfeld and Vladut, and this bound is achieved when the size of the finite field is square. When the size of the finite field is not a square, all that is known are lower bounds on the values of the function. In this thesis, we present some improvements on the known explicit lower bounds for the Ihara function when the size of the finite field is a small prime.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Asymptotically good towers; Global function fields; Ihara function; Number theory
Title
Asymptotically good towers of global function fields and bounds for the Ihara function
Author
Hall-Seelig, Laura
Number of pages
136
Publication year
2009
Degree date
2009
School code
0118
Source
DAI-B 70/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781109352054
Advisor
Hajir, Farshid
Committee member
Moll, Robert; Weston, Tom; Wong, Siman
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3372263
ProQuest document ID
304927456
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304927456
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