Asymptotically good towers and differential equations

2005/11/01 by Peter Beelen, Irene I. Bouw
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Advanced Algebra and Geometry

paper · pdf · doi:10.1112/s0010437x05001624

Abstract

This paper concerns towers of curves over a finite field with many rational points, following Garcia–Stichtenoth and Elkies. We present a new method to produce such towers. A key ingredient is the study of algebraic solutions to Fuchsian differential equations modulo p. We apply our results to towers of modular curves, and find new asymptotically good towers.

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