Updated on 2024/08/29

写真a

 
MURABAYASHI,Naoki
 
Organization
Faculty of Engineering Science Professor
Title
Professor
Contact information
メールアドレス
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Degree

  • 博士（理学） ( 1992 )

Research Interests

  • ;

Research Areas

  • Natural Science / Algebra

Education

  • Waseda University   Graduate School, Division of Science and Engineering

    - 1992

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  • Waseda University   Faculty of Science and Engineering

    - 1987

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    Country： Japan

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  • Waseda University   Graduate School, Division of Science and Engineering

    1992

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    Country： Japan

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Papers

  • On supersingular primes of the Elkies' elliptic curve Reviewed

    村林 直樹

    Funct. Approx. Comment. Math.   60.1, 41-59   2019.3

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  • On torsion points of certain CM elliptic curves Reviewed

    Naoki Murabayashi

    Functiones et Approximatio, Commentarii Mathematici   47 ( 1 )   89 - 93   2012

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Adam Mickiewicz University Press  

    Let E be a CM elliptic curve defined over an algebraic number field F with CM by an imaginary quadratic field K. We determine the group of KabF-rational torsion points of E. In some cases we also determine the group of F or KF-rational torsion points of E.

    DOI： 10.7169/facm/2012.47.1.8

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  • Determination of simple CM abelian surfaces defined over Q Reviewed

    Naoki Murabayashi

    MATHEMATISCHE ANNALEN   342 ( 3 )   657 - 671   2008.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    It is known that in the moduli space A(1) of elliptic curves, there exist precisely nine Q-rational points represented by an elliptic curve with complex multiplication by the maximal order of an imaginary quadratic field. In Murabayashi and Umegaki (J Algebra 235: 267-274, 2001) and Umegaki [Determination of all Q-rational CM-points in the moduli spaces of polarized abelian surfaces, Analytic number theory (Beijng/Kyoto, 1999). Dev. Math., vol 6. Kluwer, Dordrecht, pp 349-357, 2002] we determined all Q-rational points in A2(d) (the moduli space of d-polarized abelian surfaces) represented by a d-polarized abelian surface whose endomorphism ring is isomorphic to the maximal order of a quartic CM-field by using the result in Murabayashi (J Reine Angew Math 470: 1-26, 1996). In this paper, we prove that polarized abelian surfaces corresponding to these Q-rational CM points have a Q-rational model by constructing certain Hecke characters.

    DOI： 10.1007/s00208-008-0251-2

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  • Modularity of CM elliptic curves over division fields Reviewed

    Naoki Murabayashi

    JOURNAL OF NUMBER THEORY   128 ( 4 )   895 - 897   2008.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let E be a CM elliptic curve defined over an algebraic number field F. In general E will not be modular over F. In this paper, we determine extensions of F, contained in suitable division fields of E, over which E is modular. Under some weak assumptions on E, we construct a minimal subfield of division fields over which E is modular. (c) 2007 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jnt.2007.01.011

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  • On construction of certain CM elliptic curves Reviewed

    Naoki Murabayashi

    JOURNAL OF NUMBER THEORY   128 ( 3 )   576 - 588   2008.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let E be a CM elliptic curve defined over an algebraic number field F. In the previous paper [N. Murabayashi, On the field of definition for modularity of CM elliptic curves, J. Number Theory 108 (2004) 268-286], we gave necessary and sufficient conditions for E to be modular over F, i.e. there exists a normalized newform f of weight two on Gamma(1) (N) for some N such that Hom(F) (E, J(f)) not equal {0}. We also determined the multiplicity of E as F-simple factor of Jf when HomF (E, J(f)) not equal {0}. In this process we separated into the three cases. In this paper we construct certain CM elliptic curves which satisfy the conditions of each case. In other words, we show that all three cases certainly occur. (c) 2007 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jnt.2007.04.017

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  • On QM-abelian surfaces with model of GL(2)-type over Q Reviewed

    N Murabayashi

    JOURNAL OF NUMBER THEORY   112 ( 1 )   116 - 188   2005.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    The purpose of this paper is to characterize QM-abelian surfaces which has a model of GL(2)-type over Q. The "special" involutions on a corresponding indefinite quaternion algebra (which is defined in Section 2) play an essential role in this paper. (c) 2004 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jnt.2004.07.018

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  • On the field of definition for modularity of CM elliptic curves Reviewed

    N Murabayashi

    JOURNAL OF NUMBER THEORY   108 ( 2 )   268 - 286   2004.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

    The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition. (C) 2004 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.jnt.2004.05.004

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  • Determination of all Q-rational CM-points in moduli spaces of polarized abelian surfaces Reviewed

    A Umegaki

    ANALYTIC NUMBER THEORY   6   349 - 357   2002

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER  

    It is known that in the moduli space A, of elliptic curves, there exist precisely 9 Q-rational points corresponding to the isomorphism class of elliptic curves with complex multiplication by the ring of integers of an imaginary quadratic field. We consider the same determination problem in the case of dimension two. In the moduli space of principally polarized abelian surfaces, this problem was solved in [3]. In this paper, we shall determine all Q-rational points corresponding to the isomorphism class of abelian surfaces whose endomorphism ring is isomorphic to the ring of integers of a quartic CM-field in the non-principal case.

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  • Determination of All Q-rational CM-Points in the Moduli Space of Principally Polarized Abelian Surfaces. Reviewed

    MURABAYASHI Naoki

    Journal of Algebra   235/, 267-274   267 - 274   2001

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  • A remark on the modularity of Abelian varieties of GL(2)-type over Q Reviewed

    N Murabayashi

    JOURNAL OF NUMBER THEORY   82 ( 2 )   288 - 298   2000.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC  

    Let A be an abelian variety of GL(2)-type over the rational number field Q, without complex multiplication. In this paper, we will show that a modularity of A over the complex number field C implies that of A over Q. (C) 2000 Academic Press.

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  • Modular equations of hyperelliptic X-0(N) and an application Reviewed

    T Hibino, N Murabayashi

    ACTA ARITHMETICA   82 ( 3 )   279 - 291   1997

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：POLISH ACAD SCIENCES INST MATHEMATICS  

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  • The field of moduli of Abelian surfaces with complex multiplication Reviewed

    N Murabayashi

    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK   470   1 - 26   1996

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：WALTER DE GRUYTER & CO  

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  • SHIMURA CURVES AS INTERSECTIONS OF HUMBERT SURFACES AND DEFINING EQUATIONS OF QM-CURVES OF GENUS-2 Reviewed

    K HASHIMOTO, N MURABAYASHI

    TOHOKU MATHEMATICAL JOURNAL   47 ( 2 )   271 - 296   1995.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TOHOKU UNIVERSITY MATHEMATICAL INSTITUTE  

    Shimura curves classify isomorphism classes of abelian surfaces with quaternion multiplication. in this paper, we are concerned with a fibre space, the base space of which is a Shimura curve and fibres are curves of genus two whose jacobian varieties are abelian surfaces of the above type. We shall give an explicit defining equation for such a fibre space when the discriminant of the quaternion algebra is 6 or 10.

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  • THE MODULI SPACE OF CURVES OF GENUS 2 COVERING ELLIPTIC-CURVES Reviewed

    N MURABAYASHI

    MANUSCRIPTA MATHEMATICA   84 ( 2 )   125 - 133   1994.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER VERLAG  

    We consider the moduli space S(n) of curves C of genus 2 with the property: C has a ''maximal'' map f of degree n to an elliptic curve E. Here, the term ''maximal'' means that the map f : C --> E doesn't factor over an unramified cover of E. By Torelli map S(n) is viewed as a subset of the moduli space A2 of principally polarized abelian surfaces. On the other hand the Humbert surface H(DELTA) of invariant DELTA is defined as a subvariety of A2(C), the set of C-valued points of A2. The purpose of this paper is to relate S(n) with H(DELTA).

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  • MORDELL-WEIL RANK OF THE JACOBIANS OF THE CURVES DEFINED BY Y(P)=F(X) Reviewed

    N MURABAYASHI

    ACTA ARITHMETICA   64 ( 4 )   297 - 302   1993

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：POLISH ACAD SCIENCES INST MATHEMATICS  

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  • ON NORMAL FORMS OF MODULAR-CURVES OF GENUS-2 Reviewed

    N MURABAYASHI

    OSAKA JOURNAL OF MATHEMATICS   29 ( 2 )   405 - 418   1992.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：OSAKA JOURNAL OF MATHEMATICS  

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  • Cyclotomic function fields with divisor class number one Reviewed

    Masanari Kida, Naoki Murabayashi

    Tokyo Journal of Mathematics   14 ( 1 )   45 - 56   1991

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.3836/tjm/1270130486

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Books

  • Dirichlet's theorem on arithmetic progressions

    MURABAYASHI,Naoki（ Role： Sole author）

    2011.11 

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Presentations

  • 特殊関数 e^x E_1(x) の連分数展開とその収束性および Euler-Gompertz 定数 \delta の無理性への応用

    村林直樹, 吉田颯飛

    2022 大分熊本整数論研究集会  2022.9 

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    Event date： 2022.9

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  • On supersingular primes of the Elkies' elliptic curve

    2016.10 

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    Event date： 2016.10

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  • On torsion points of CM elliptic curves

    村林 直樹

    Japan-Korea Number Theory Seminar 2011  2011.11 

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    Venue：Nagoya University, Higashiyama Campus, Noyori Conference Hall  

    2011 年11 月9日から12日に亘って名古屋大学で開催された Japan-Korea Number Theory Seminar 2011 に於いて研究成果を発表した。なお、この研究集会の報告集はない。

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  • ある楕円曲線の supersingular primes について

    村林 直樹

    「数論と社会に役立つ数学」研究集会  2010.8 

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    Venue：室蘭工業大学工学部 Ｑ 棟（教育・研究２号館）４階Ｑ４０２室  

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Research Projects

  • 虚数乗法論とKP方程式の関連について

    2003 - 2005

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    Grant type：Competitive

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  • QM型アーベル曲面のHasse-Weilゼータ関数について

    1996 - 1998

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    Grant type：Competitive

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  • 有理数体上定義されたCM型アーベル曲面の分類

    1995

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    Grant type：Competitive

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Devising educational methods

  • 教科書に沿って進め、教科書では証明を省略している箇所を丁寧に解説している。数学の専門書を自分で読んで身につけるための極意である「行間を埋めながら読み進む」を実践することで、学生に数学の専門書の読み方を身に付けさせるのが狙いである。また、板書は出来るだけ丁寧にすることにより、学生が復習をする際の手助けになるようにしている。

Teaching materials

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Teaching method presentations

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Special notes on other educational activities

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