Algebraic Curves, Riemann hypothesis and coding

Marios Magioladitis

This essay is my diploma thesis and was presented on Thursday November 29th 2001. The supervisor was professor J.A. Antoniadis. The evaluation committee consisted also of Alexis Kouvidakis and Aristides Kontogeorgis.

The purpose of this essay is to show the usefulness of studying algebraic curves over finite fields, as far as Number Theory problems and Coding Theory are concerned. It contains a thorough treatment of Manin's proof of Hasse's theorem, which is a special case of Riemann Hypothesis for finite fields, and also examples of constructing algebraic geometry codes.

In the first chapter we discuss basic properties of the theory of algebraic curves. In the second chapter we study elliptic curves over finite fields. In the third chapter we state basic notions of coding theory, some additional elements of algebraic curves theory and the essay ends with the detailed presentation of two algebraic geometry codes.

See full introduction and contents in English: [html] [doc] [ps]

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In Word documents:

Full/ZIP	Greek	English	[90 pages / 337 Kb]
Introduction/Contents/Chapter 1	Greek	English	[26 pages / 258 Kb]
Chapters 2-3/Bibliography/Index	Greek	English	[64 pages / 1,259 Kb]

In PDF format:

Full/ZIP	Greek		[90 pages / 717 Kb]
Introduction/Contents/Chapter 1	Greek	English (p. 27-90)	[90 pages / 761 Kb]
Chapters 2-3/Bibliography/Index

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Last update: November 22, 2003