A DRINFELD MODULAR INTERPRETATION OF AN ASYMPTOTICALLY OPTIMAL TOWER OF CURVES OVER FINITE FIELDS

Türkü Özlüm Çelik
Mathematics, MSc. Thesis, 2015

Thesis Jury

Assoc. Prof. Cem Güneri (Thesis Advisor),

Asst. Prof. Kağan Kurşungöz,

Prof. Dr. Henning Stichtenoth,

Prof. Dr. Alev Topuzoğlu,

Assoc. Prof. Hüsnü Yenigün

Date &Time: January 05th, 2015 –  18:00

Place: Sabancı University, FENS L062
Keywords : Drinfeld Modular Curves

Abstract

In this thesis, we study a Drinfeld modular interpretation due to Elkies of an asymptotically optimal tower that was constructed by Bezerra and Garcia.

We explain what an asymptotically optimal tower over a finite field Fq is and give the definition of the asymptotically optimal tower given by Bezerra and Garcia.

We give some basic facts about Drinfeld modules. Additionally, we present the analytical theory of Drinfeld modules using lattices and exponential functions to better understand the analogy with the classical theory.

We exhibit the Drinfeld modular curves that give the tower of Bezerra and Garcia. Hence we see an Drinfeld modular interpretaion of this tower.