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Date of Award
5-2009
Access Type
Campus Access
Document type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics and Statistics
First Advisor
Farshid Hajir
Second Advisor
Tom Weston
Third Advisor
Siman Wong
Subject Categories
Mathematics
Abstract
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.
DOI
https://doi.org/10.7275/5649557
Recommended Citation
Hall-Seelig, Laura, "Asymptotically Good Towers Of Global Function Fields And Bounds For The Ihara Function" (2009). Doctoral Dissertations 1896 - February 2014. 90.
https://doi.org/10.7275/5649557
https://scholarworks.umass.edu/dissertations_1/90