Proceedings of International Mathematical Sciences

Proceedings of International Mathematical Sciences

The Hasse-Minkowski Theorem and Legendre's Theorem for Quadratic Forms in Two and Three Variables

Yazarlar: Phuc NGO, Mehmet DİK

Cilt 2 , Sayı 2 , 2020 , Sayfalar 79 - 89

Konular:Bilgisayar Bilimleri, Disiplinler Arası Uygulamalar

DOI:10.47086/pims.827611

Anahtar Kelimeler:Hasse-Minkowski,Quadratic form,Algorithm

Özet: Determining the solvability of equations has been an extended and fundamental study in Mathematics. The local-global principle states two objects are equivalent globally if and only if they are equivalent locally at all places. By applying this principle, the Hasse - Minkowski theorem is able to identify the existence of rational solutions of an equation. This paper explores the applications of the Hasse-Minkowski theorem to homogeneous quadratic forms in two and three variables. After providing some of the necessary proofs and definitions, we have been able to introduce some complete computer programs implementing the Hasse-Minkowski theorems and Legendre theorem with some supporting functions like the Eratosthenes sieve.

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@article{2020, title={The Hasse-Minkowski Theorem and Legendre’s Theorem for Quadratic Forms in Two and Three Variables}, volume={2}, number={79–89}, publisher={Proceedings of International Mathematical Sciences}, author={Phuc NGO,Mehmet DİK}, year={2020} }
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Phuc NGO,Mehmet DİK. (2020). The Hasse-Minkowski Theorem and Legendre’s Theorem for Quadratic Forms in Two and Three Variables (Vol. 2). Vol. 2. Proceedings of International Mathematical Sciences.
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Phuc NGO,Mehmet DİK. The Hasse-Minkowski Theorem and Legendre’s Theorem for Quadratic Forms in Two and Three Variables. no. 79–89, Proceedings of International Mathematical Sciences, 2020.
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