Browsing Matematik by Author "Özman, Ekin."

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  • ABC conjecture and its implications 
    Koç, Tuğçe. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, our aim is to state the importance of abc conjecture and prove the strong results we obtain with the help of abc conjecture. First, we give necessary notions and tools which are used throughout the thesis. ...
  • Class number one problem 
    Kır, Harun. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In 1801, Gauss conjectured that there are exactly nine imaginary quadratic number fields with class number one, namely: Q(√−1), Q(√−2), Q(√−3), Q(√−7), Q(√−11), Q(√−19), Q(√−43), Q(√−67) and Q(√−163). This conjecture is ...
  • Different versions of the modularity theorem 
    Bildik, İlkiz. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    One of the most interesting results in number theory is the proof of the Modu larity Theorem. The Modularity Theorem has many different versions. The geometric version states that there is a surjective morphism between ...
  • Inverse galois problem 
    Kırımlı, Eda. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    The main focus of this thesis is so called Inverse Galois Problem. The statement of the problem is that given a finite group G, does there exist a finite Galois extension L/Q whose Galois group is G? There has been a great ...
  • Modular approcah to diophantine equations 
    Işık, Erman. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, we study the modular approach to the Fermat’s equation xp+yp = zp, where x,y and z are co-prime integers, and p is a prime, and some generalizations. After reviewing and explaining how the modular approach ...
  • Monogenic number fields 
    Değirmenci, Pınar. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)
    Determining whether the ring of integers OK of an algebraic number field K of degree n admits a power integral basis is one of the classic problems in algebraic number theory. In other words, we want to determine whether ...
  • The ordinary component of l-isogeny graph of elliptic curves 
    Kaytancı, Kübra. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis, our aim is to understand `-volcanoes which are ordinary compo nents of `-isogeny graphs of elliptic curves over finite fields under certain conditions. In 1996, the structure of isogeny graphs of elliptic ...

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