Off-campus UMass Amherst users: To download campus access dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.
Date of Award
Doctor of Philosophy (PhD)
Mathematics and Statistics
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.
Hall-Seelig, Laura, "Asymptotically Good Towers Of Global Function Fields And Bounds For The Ihara Function" (2009). Doctoral Dissertations 1896 - February 2014. 90.