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BİZİM, OSMAN

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BİZİM

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OSMAN

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    Publication
    A constructive method for the cycloidal normal free subgroups of finite index of hecke groups H (√2) AND H (√3)
    (Acad Sinica, 2006-09-01) DOĞAN, SETENAY; DEMİRCİ, MUSA; Demirci, Musa; Cangül, İsmail Naci; CANGÜL, İSMAİL NACİ; Bizim, Osman; BİZİM, OSMAN; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-0700-5774; A-6557-2018; AAH-1468-2021; AAH-9762-2021; J-3505-2017; ABA-6206-2020
    Cycloidal subgrups of the modular group are studied in [8]. Here cycloidal free normal subgroups of Hecke groups are considered. It is found that when q equivalent to 2 ( mod 4), H ( lambda(q)) has no such subgroups. In all other cases the signatures of these subgroups are constructed by means of q-gons and their signatures are given.
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    Publication
    On the product of translated division polynomials and somos sequences
    (Wydawnictwo Naukowe Uam, 2023-09-01) Gezer, Betül; Bizim, Osman; GEZER, BETÜL; BİZİM, OSMAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; AAH-1547-2021; AAH-1468-2021
    We consider the product sequences of the sequences (psi n(P)), (phi n(P)), and (omega n(P)) (n is an element of N) of values of the translated division polynomials of an elliptic curve E/K evaluated at a point P is an element of E(K)2. We prove that these sequences are purely periodic when K is a finite field. Then we use p-adic properties of these sequences to obtain p-adic convergence of product of the Somos 4 and Somos 5 sequences.
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    Publication
    Sequences generated by elliptic curves
    (Polish Acad Sciences Inst Mathematics-IMPAN, 2019-01-01) Gezer, Betül; Bizim, Osman; GEZER, BETÜL; BİZİM, OSMAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; AAH-1468-2021; AAH-1547-2021
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    Publication
    Representations of positive integers by positive quadratic forms
    (Southeast Asian Mathematical Soc-seams, 2011-01-01) TEKCAN, AHMET; Gezer, Betül; GEZER, BETÜL; Bizim, Osman; BİZİM, OSMAN; Özkoç, Arzu; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; AAH-1468-2021; AAH-8518-2021; AAH-1547-2021
    In this work we consider the representations of positive integers by quadratic forms F-1 = x(1)(2) + x(1)x(2) + 8x(2)(2) and G(1) = 2x(1)(2) + x(1)x(2) + 4x(2)(2) of discriminant 31 and we obtain some results concerning the modular forms (sci) (T; F, phi(tau s)). Moreover we construct a basis for the cusp form space S-4 (Gamma(0) (31), 1), and then we give some formulas for the number of representations of positive integer n by positive definite quadratic forms.
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    Publication
    Corrigendum on "the number of points on elliptic curves E : y2 = x3
    (Korean Mathematical Soc, 2007-01-01) İnam, İlker; Soydan, Gökhan; SOYDAN, GÖKHAN; CANGÜL, İSMAİL NACİ; Bizim, Osman; BİZİM, OSMAN; Demirci, Musa; DEMİRCİ, MUSA; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5765-1718; 0000-0002-0700-5774; M-9459-2017; ABA-6206-2020; A-6557-2018; AAH-1468-2021
    In this work, authors considered a result concerning elliptic curves y(2) = x(3) + ex over F-p mod 8, given at [1]. They noticed that there should be a slight change at this result. They give counterexamples and the correct version of the result.