Sonlu cisimler üzerinde frey eliptik eğrileri
The Frey elliptic curves on finite fields
- Tez No: 180126
- Danışmanlar: PROF. DR. İSMAİL NACİ CANGÜL
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2006
- Dil: Türkçe
- Üniversite: Balıkesir Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 106
Özet
In this thesis, the number of rational points, their orders, and the group structure of them, on Frey elliptic curves 2 32 y x nx = − which are the special case of simplified Weierstrass equation over finite fields Fp where p is prime, are studied. This study consists of five chapters. In the first chapter, which is the introductory chapter of this thesis, the thesis is introduced. In the second chapter, the necessary definitions and results are recalled. In the third chapter, some new results concerning the number of points on the Frey elliptic curves 2 32 y x nx = − are given. In the fourth chapter, the group structures of the Frey elliptic curves 2 32 y x nx = − on finite fields Fp are obtained. It is shown that the group structure of these curves can be of two types according to that p is a prime congruent to 1 or 3 modulo 4. It has been shown that, in the former case, the group structure of rational points on the curve En is isomorphic to . ( ) En p a ab F ZZ ≅ × , where a b, + ∈` . While considering the group structure of these curves, the number of rational points is also studied. Further, it has also been shown that whether the group has elements of order 4 according to whether n is in Qp or not. In the fifth chapter, the results obtained in the thesis are recalled. KEY WORDS: elliptic curves over finite fields / rational points / cubic equations / Frey elliptic curves.
Özet (Çeviri)
Özet çevirisi mevcut değil.
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