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Research Activity

Field of Study

Number Theory

Subject of Study

Algebraic stucture of number fields (unit group, class group, diophantine equation)

Book / Paper

Book:

1.Shin-ichi Katayama :
Proceedings of the 2003 Nagoya conference Yokoi-Chowla conjecture and related problems,
Furukawa Total Printing, Saga, Mar. 2004.

Academic Paper (Judged Full Paper):

1.Shin-ichi Katayama, Toru Nakahara, Nadia Khan and Takeshi Uehara :
Monogenity of totally real algebraic extension fields over a cyclotomic fields,
Journal of Number Theory, Vol.158, 348-355, 2016.
(DOI: 10.1016/j.jnt.2015.06.018,   Thomson Reuters: Web of Science™,   Elsevier: Scopus)
2.Shin-ichi Katayama :
On Zenkoku Shijyo Suugaku Danwakai and Shikoku Suugaku Shijyo Danwa,
Natural Science Research, Faculty of Integrated Arts and Sciences, The University of Tokushima, Vol.28, No.4, 37-43, 2014.
3.Shin-ichi Katayama, Toru Nakahara, Ali Syed Inaya Shah, Mohammad Khalid and Sareer Badhah :
Orbit of quadratic irrationals molulo p by the modular group,
Journal of Research, Vol.25, No.1, 1-5, 2009.
4.Shin-ichi Katayama and Yasuhiro Kishi :
Infinite family of imaginary cyclic fields of degree p-1 with the p-rank of the ideal class groups of at least two,
Tsinghua Science & Technology, Vol.12, No.4, 475-478, 2007.
(DOI: 10.1016/S1007-0214(07)70070-6,   Elsevier: Scopus)
5.Shin-ichi Katayama, Claude Levesque and Toru Nakahara :
On a family of real bicyclic biquadartic fields,
CRM Proceedings and Lecture Notes, Vol.36, 165-174, 2004.
6.Shin-ichi Katayama and Claude Levesque :
On simultaneous diophantine equations,
Acta Arithmetica, Vol.108, No.4, 369-377, 2003.
(DOI: 10.4064/aa108-4-6,   CiNii: 120004211201,   Thomson Reuters: Web of Science™,   Elsevier: Scopus)
7.Shin-ichi Katayama :
On zeta functions associated to finite groups,
Advanced Studies in Contemporary Mathematics, Vol.4, No.2, 111-125, 2002.
8.Shin-ichi Katayama, Claude Levesque and Toru Nakahara :
On the unit group and the class number of certain composita of two real quadratic fields,
Manuscripta Mathematica, Vol.105, No.1, 85-101, 2001.
(DOI: 10.1007/s002290170011,   Elsevier: Scopus)
9.Shin-ichi Katayama :
The abc conjecture, fundamental units and the simultaneous Pell equations,
Proceedings of the Jangjeon Mathematical Society, Vol.1, 19-26, 2000.
10.Shin-ichi Katayama :
The abc conjecture and the fundamental system of units of certain real bicyclic biquadratic fields,
Proceedings of the Japan Academy. Series A, Mathematical Sciences, Vol.75A, No.10, 198-199, 2000.
(DOI: 10.3792/pjaa.75.198,   Thomson Reuters: Web of Science™,   Elsevier: Scopus)
11.Shin-ichi Katayama, Claude Levesque and Toru Nakahara :
On the units and class numbers of certain composita of two quadratic fields,
Proceedings of the Japan Academy, Vol.75A, No.4, 63-66, 1999.
12.Shin-ichi Katayama :
Real quadratic fields of Richaud-Degert type and related topics,
Advanced Studies in Contemporary Mathematics, Vol.1, 17-33, 1999.
13.Shin-ichi Katayama :
Remark on upper bounds for L(1,/chi),
Proceedings of the Japan Academy, Vol.72A, No.4, 89-90, 1996.
14.Shin-ichi Katayama and Yoko Kikuchi :
Some remarks on Egyptian fractions,
Mathematica Japonica, Vol.42, No.1, 127-130, 1995.
15.Shin-ichi Katayama and Shigeru Katayama :
Fibonacci, Lucas and Pell numbers and class numbers of bicyclic biquadratic fields,
Mathematica Japonica, Vol.42, No.1, 121-126, 1995.
16.Shin-ichi Katayama and Shigeru Katayama :
On bound functions of fundamental units of real quadratic fields,
Journal of Number Theory, Vol.46, No.3, 385-390, 1994.
17.Shin-ichi Katayama :
Group rings and the norm groups,
Proceedings of the Japan Academy, Vol.69A, No.9, 363-367, 1993.
18.Shin-ichi Katayama :
On fundamental units of real quadratic fields with norm +1,
Proceedings of the Japan Academy, Vol.68A, No.1, 18-20, 1992.
19.Shin-ichi Katayama :
On fundamental units of real quadratic fields with norm -1,
Proceedings of the Japan Academy, Vol.67A, No.10, 343-345, 1992.
20.Shin-ichi Katayama :
Isogenous tori and the class number formulae,
Journal of Mathematics of Kyoto University, Vol.31, No.3, 679-694, 1991.
21.Shin-ichi Katayama and Shigeru Katayama :
A note on the problem of Yokoi,
Proceedings of the Japan Academy, Vol.67A, No.1, 26-28, 1991.
22.Shin-ichi Katayama :
On products of consecutive integers,
Proceedings of the Japan Academy, Vol.66A, No.10, 305-306, 1991.
23.Shin-ichi Katayama and Shigeru Katayama :
On certain real quadratic fields with class numbers 3 and 5,
Proceedings of the Japan Academy, Vol.66A, No.9, 300-303, 1990.
24.Shin-ichi Katayama :
E(K/k) and other arithmetical invariants for finite Galois extensions,
Nagoya Mathematical Journal, Vol.114, 135-142, 1989.
25.Shin-ichi Katayama :
On unit groups of algebraic number fields,
Proceedings of the Japan Academy, Vol.64A, No.9, 345-346, 1988.
26.Shin-ichi Katayama :
The Euler number and other arithmetical invariants for finite Galois extensions of algebraic number fields,
Proceedings of the Japan Academy, Vol.63A, No.2, 27-30, 1987.
27.Shin-ichi Katayama :
Class number relations of algebraic tori II,
Proceedings of the Japan Academy, Vol.62A, No.8, 320-322, 1986.
28.Shin-ichi Katayama :
Class number relations of algebraic tori I,
Proceedings of the Japan Academy, Vol.62A, No.6, 216-218, 1986.
29.Shin-ichi Katayama :
A theorem on the cohomology of groups and some arithmetical applications,
Journal of Mathematics of Kyoto University, Vol.25, No.2, 365-391, 1985.
30.Shin-ichi Katayama :
On homotopy classes of cochain maps,
Proceedings of the Japan Academy, Vol.61A, No.5, 147-148, 1985.
31.Shin-ichi Katayama :
On the Tamagawa number of algebraic tori,
数学, Vol.37, No.1, 81-83, 1985.
32.Shin-ichi Katayama :
Cohomology groups of the unit group of a local field,
Proceedings of the Japan Academy, Vol.58A, No.9, 406-409, 1982.
33.Shin-ichi Katayama :
On the Galois cohomology groups of CK / DK,
Japanese Journal of Mathematics, Vol.8, No.2, 407-415, 1982.
34.Shin-ichi Katayama :
On the Galois cohomology groups of CK / DK,
Proceedings of the Japan Academy, Vol.57A, No.7, 378-380, 1981.

Academic Paper (Unrefereed Paper):

1.Shin-ichi Katayama :
石原侑氏の数学史論文について,
徳島科学史雑誌, Vol.35, 63-65, 2016.
2.Shin-ichi Katayama :
Hypothesis of Schinzel and Sierpinski and Cyclotomic Fields with Isomorphic Galois Groups,
Journal of Mathematics, The University of Tokushima, Vol.50, 43-47, 2016.
3.Shin-ichi Katayama :
Products of Arithmetic Progressions which are Squares,
Journal of Mathematics, The University of Tokushima, Vol.49, 9-12, 2015.
4.Shin-ichi Katayama :
Diophantine Equations and Hilbert's Theorem90,
Journal of Mathematics, The University of Tokushima, Vol.48, 37-42, 2014.
5.Shin-ichi Katayama :
フィボナッチの円周率の計算について,
徳島科学史雑誌, Vol.32, 1-8, 2013.
6.Shin-ichi Katayama :
Modified Farey trees and Pythagorean triples,
Journal of Mathematics, The University of Tokushima, Vol.47, 1-13, 2013.
(CiNii: 120005352806)
7.Shin-ichi Katayama :
Scissors congruence for certain k-polygons,
Journal of Mathematics, The University of Tokushima, Vol.46, 1-12, 2012.
(CiNii: 110009514554)
8.Shin-ichi Katayama :
Generalized Goggins's formula for Lucas and Companion Lucas sequences,
Journal of Mathematics, The University of Tokushima, Vol.45, 19-25, 2011.
(CiNii: 110008729447)
9.Shin-ichi Katayama and Takuya Doi :
On partitions and k-polygons,
Journal of Mathematics, The University of Tokushima, Vol.44, 13-25, 2010.
(CiNii: 110007870530)
10.Shin-ichi Katayama and Arata Kuroki :
A variation of Takagi's proof for quadratic reciprocity laws for Jacobi symbols,
Journal of Mathematics, The University of Tokushima, Vol.43, 9-23, 2009.
(CiNii: 110007492238)
11.Shin-ichi Katayama and Takuya Doi :
A remark on partitions and triangles,
Journal of Mathematics, The University of Tokushima, Vol.43, 1-7, 2009.
(CiNii: 110007492212)
12.Shin-ichi Katayama :
On some formulas for π/2,
Journal of Mathematics, The University of Tokushima, Vol.42, 13-17, 2008.
(CiNii: 110007127172)
13.Shin-ichi Katayama :
Some infinite series of Fibonacci numbers,
Journal of Mathematics, The University of Tokushima, Vol.42, 9-12, 2008.
(CiNii: 110007127173)
14.Shin-ichi Katayama :
On finite simple groups of cube order,
Journal of Mathematics, The University of Tokushima, Vol.41, No.0, 25-31, 2007.
(CiNii: 110006853379)
15.Shin-ichi Katayama :
On the diophantine equation (x^2+1)(y^2+1)=(z^2+1)^2,
Journal of Mathematics, The University of Tokushima, Vol.40, 9-14, 2006.
(CiNii: 110004849832)
16.Shin-ichi Katayama :
Maps R:Z/nZ → Z/n^2Z and some cryptographic applications,
Journal of Mathematics, The University of Tokushima, Vol.39, 7-21, 2005.
17.Shin-ichi Katayama :
A conjecture on fundamental units of real quadratic fields,
Journal of Mathematics, The University of Tokushima, Vol.35, 9-15, 2002.
18.Shin-ichi Katayama :
Zeta functions of finite groups and arithmetically equivalent fields,
Journal of Mathematics, The University of Tokushima, Vol.35, 1-8, 2002.
19.Shin-ichi Katayama :
Several methods for solving simultaneous Fermat-Pell equations,
Journal of Mathematics Tokushima University, Vol.33, 1-14, 2000.
20.Shin-ichi Katayama :
On the class numbers of real quadratic fields of Richaud-Degert type,
Journal of Mathematics Tokushima University, Vol.31, 1-6, 1998.
21.Shin-ichi Katayama :
Unit groups of some quartic fields,
Journal of Mathematics Tokushima University, Vol.28, 1-4, 1995.
22.Shin-ichi Katayama and Shigeru Katayama :
On certain real bicyclic biquadratic fields with class number one and two,
Journal of Mathematics Tokushima University, Vol.26, 1-8, 1993.
23.Shin-ichi Katayama and Kenji Kashihara :
On the structure of the integer solutions of z^2=(x^2-1)(y^2-1)+a,
Journal of Mathematics Tokushima University, Vol.24, 1-11, 1991.

Review, Commentary:

1.Shin-ichi Katayama :
小出由岐太の求玉道間数法,
徳島新聞, Jul. 2017.
2.Shin-ichi Katayama :
海野十三と虫食い算,
徳島新聞, May 2015.
3.Shin-ichi Katayama :
海野十三と暗号,
徳島新聞, May 2014.
4.Shin-ichi Katayama :
マルコフ数の問題,
数学セミナー, Vol.52, No.52, 18-24, Jul. 2013.
(CiNii: 40019703128)

Proceeding of International Conference:

1.Shin-ichi Katayama :
On finite simple groups of power order,
Hawaii Conference in Algebraic Number Theory, Arithmetic Geometry, and Modular Forms, Honolulu, Mar. 2012.
2.Shin-ichi Katayama :
On finite simple groups of square order,
1078th American Mathematical Society Sectional Meeting, Honolulu, Mar. 2012.
3.Shin-ichi Katayama :
On a family of simultaneous Pell equations,
The seventh Japan-Korea Number Theory Symposium, Kujyu, Oct. 2004.
4.Shin-ichi Katayama and Yasuhiro Kishi :
An infinite family of imaginary cyclic fields of degree p-1 which have ideal class groups of p-ranks greater than one,
Yokoi-Chowla conjecture and related problems, Nagoya, Oct. 2003.
5.Shin-ichi Katayama :
Zeta functions of finite groups and arithmetically equivalent fields,
Seaway Number Theory Conference, Otawa (Canada), May 2001.
6.Shin-ichi Katayama :
The abc conjecture, fundamental units and the simultaneous Pell equations,
The fifth Japan-Korea Number Theory Symposium, Sendai, Nov. 1999.
7.Shin-ichi Katayama :
Units of certain quartic fields and integer points on an elliptic curve,
Workshop on Number Theory, Tokyo, Jul. 1999.
8.Shin-ichi Katayama :
Squares in Fibonacci sequence and unit indices of the biquadratic fields,
3rd Japan-Korea Symposium on Number Theory, Pohang(Korea), Jul. 1997.
9.Shin-ichi Katayama :
On composite real quadratic fields with class number one,
2nd Japan-Korea Symposium on Number Theory, Saga, Dec. 1996.
10.Shin-ichi Katayama :
Real quadratic fields of Richaud-Degert type and related topics,
1st Japan-Korea Symposium on Number Theory, Hapchun(Korea), Jul. 1996.

Proceeding of Domestic Conference:

1.Shin-ichi Katayama and 久保 智哉 :
取る石の数に制限のあるWythoffの二山崩し,
日本フィボナッチ協会/研究集会, Aug. 2017.
2.Shin-ichi Katayama, Kosuke Ono, 住 彩花, 近藤 彰 and 松澤 康平 :
海野十三と暗号,虫食い算,
海野十三忌2016, May 2016.
3.Shin-ichi Katayama, Kosuke Ono, 住 彩花, 近藤 彰 and 松澤 康平 :
海野十三と数学パズル,
日本科学史学会第19回西日本研究集会, Nov. 2015.
4.Shin-ichi Katayama :
NSW素数について,
日本フィボナッチ協会/研究集会, Aug. 2015.
5.Shin-ichi Katayama :
フィボナッチの著作と円周率計算,
日本フィボナッチ協会/研究集会, Aug. 2014.
6.Shin-ichi Katayama :
海野十三の暗号小説について,
日本科学史学会四国支部総会, Aug. 2014.
7.Shin-ichi Katayama :
フィボナッチの円周率の計算について,
日本科学史学会四国支部総会, Aug. 2013.
8.Shin-ichi Katayama :
On finite simple groups of power order,
Workshop in Number Theory in Saga 2011, Jan. 2011.
9.Shin-ichi Katayama :
RDタイプの実2次体のある種の分布と類数問題,
Workshop in Number Theory in Saga 2010, Jan. 2010.
10.Shin-ichi Katayama :
Class number problem of quadratic fields,
Galois theory and related problems Kanazawa 2009, Dec. 2009.
11.Shin-ichi Katayama :
Two topics on Gauss's half system,
Number Theory in Saga 2009, Jan. 2009.
12.Shin-ichi Katayama :
RDタイプの実2次体のある種の分布について,
Galois theory and related problems Tokushima 2008, Sep. 2008.
13.Shin-ichi Katayama and Hiroharu Yasui :
RSA Signatures and Redundancy,
10th Algorithm on Number Theory and Its Applications, May 2003.
14.Shin-ichi Katayama :
ABC conjecture and the fundamental system of units of certain algebraic number fields,
Inverse Galois problem and number theory, Aug. 1999.
15.Shin-ichi Katayama :
Group rings and the norm groups of cyclic extensions,
Nagoya Number Theory Seminar Spring Colloquim, Apr. 1993.

Report:

1.Shin-ichi Katayama :
Class number problem of quadratic fields,
Proceedings of the 8th Workshop on Number Theory, 81-96, Sep. 2010.
2.Shin-ichi Katayama :
On a family of simultaneous Pell equations,
Proceedings of the Japan-Korea Joint Seminar on Number Theory, 86-91, Apr. 2005.
3.Shin-ichi Katayama :
On class number one composita of real quadratic fields of Chowla-Yokoi type,
Proceedings of the 2003 conference Yokoi-Chowla conjecture and related problems, 51-58, Saga, Mar. 2004.
4.Shin-ichi Katayama, Claude Levesque and Toru Nakahara :
On the unit groups of certain quartic fields and simultaneous Fermat-Pell equations,
津田塾大学 数学·計算機科学研究所 研究所報, Vol.17, 73-82, Tokyo, Feb. 1999.
5.Shin-ichi Katayama :
On the class numbers od algebraic tori,
Proceedings of the 33th symposium on algebra, 1-12, Fukui, Jul. 1987.
6.Shin-ichi Katayama :
On the Galois cohomology groups of CK / DK,
RIMS Kokyuroku, Vol.440, 2-10, Kyoto, Jun. 1981.

Grants-in-Aid for Scientific Research (KAKEN Grants Database @ NII.ac.jp)

  • Number Theory and its Development to Discrete Mathematics (Project/Area Number: 20540019 )
  • Number Theory, Its Application to Discrete Mathematics and Development (Project/Area Number: 18540040 )
  • Number Theory and Its Applications to Discrete Mathematics (Project/Area Number: 16540029 )
  • Number Theory and Applications to the Related Discrete Mathematics (Project/Area Number: 14540033 )
  • ABC Conjecture and the Structure of Algebraic Number Fields (Project/Area Number: 14540030 )
  • Number Theory and Its Apprication to Discrete Mathematics (Project/Area Number: 11640036 )
  • 類数問題とHomology代数的構造の研究 (Project/Area Number: 07640053 )
  • シンプレクティック構造と数理物理学の研究 (Project/Area Number: 05640119 )
  • 可換環のホモロジー代数的性質の研究 (Project/Area Number: 05640048 )
  • 超函数と数理物理学の研究 (Project/Area Number: 04640165 )
  • 数理物理学とスペクトル理論の研究 (Project/Area Number: 03640163 )
  • Search by Researcher Number (70194777)