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CURRICULUM  VITAE of

Prof .  XianKe      ZHANG

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Address : Tsinghua UniversityDepartment of Mathematical Sciences, 

Beijing 100084,    P. R. China

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arrowRdong.gif (928 bytes)UNIVERSITY EDUCATION

arrowRdong.gif (928 bytes)RESEARCH

arrowRdong.gif (928 bytes)EXPERIENCE   IN HIGHER  EDUCATION

arrowRdong.gif (928 bytes)PRIZES AND AWARDS

arrowRdong.gif (928 bytes)MEMBERSHIP AND SERVICE

arrowRdong.gif (928 bytes)ACADEMIC TALKS

arrowRdong.gif (928 bytes)Writing Comments

arrowRdong.gif (928 bytes)PUBLICATIONS

arrowRdong.gif (928 bytes)Recent Publications NEWdongzi.gif (1092 bytes)

arrowRdong.gif (928 bytes)Publ.-list inMath. Reviews(partial) NEWdongzi.gif (1092 bytes)NEWdongzi.gif (1092 bytes)

arrowRdong.gif (928 bytes)Reviews by Math. Reviews(partial) NEWdongzi.gif (1092 bytes)NEWdongzi.gif (1092 bytes)

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UNIVERSITY   EDUCATION:

Ph.D.    1985:                Univ. of  Science and Tech. of China;

MA.    1982:                  Univ. of  Science and Tech. of China;

B.Sc(equi.). 1969:           Univ. of  Science and Tech. of China.                      

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RESEARCH:

Tsinghua University (1993---);

University of Science & Tech. of China (1978---1993);

University of Maryland, USA (Aug. 1987---Sept. 1988);

International Centre for Theor. Physics, Italy

(Regular Asso. Member 1991---; Senior Asso Membr 1999--);

Areas: Number Theory, Algebra, Function Fields,

Arithmetic Algebraic Geometry, Arithmetic of Elliptic Curves

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earthanim.gif (10689 bytes)EXPERIENCE  IN

HIGHER  EDUCATION:

Tsinghua University, Professor, 1993---;

Univ. Scien. & Tech. China, Professor/Asso.Prof./Instructor/Assist., 1974---93;

 

Lecture Courses:  Algebraic Number Theory;

Class Field Theory (1983--, to graduates);  Algebraic Geometry;

Elliptic Curves (1986--); Abstract Algebra, Linear Algebra, Calculus,

Complex Analysis,   Analytic Geometry,  Number Theory,

Algebraic Code Theory,  Commutative Algebra, etc.

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PRIZES AND AWARDS:

1. Be Conferred the Title ``Ph. Doctor of China Having Outstanding Merit''

        by State Education Commission & State Academic-Degree Commission, Jan. 1991

2. National Natural-Science Prize (1989, with Keqin Feng and Hongwen Lu)

3. Scientific Progress Prize (Academia Sinica, 1988, with Feng & Lu)

4. Prize of Scientific Research (Univ Sci Tech China, 1985)

5. Prize of Scientific Papers (Anhui Province, 1986)

6. Prize of   "Good Teacher and Helpful Friend of  Graduate-Students" (Tsinghua Univ. 1998)
      

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MEMBERSHIP AND SERVICE:

icon-balldong.gif (1653 bytes)International Center for Theoretical Physics (Regular Associate Member(1991--),

     Senior A. Member (1999--).

icon-balldong.gif (1653 bytes)American Mathematical Society (1985--).

icon-balldong.gif (1653 bytes)Regular Reviewer of ``Mathematical Reviews'' (USA) (1985--).

icon-balldong.gif (1653 bytes)Regular Reviewer of ``Zentralblatt fur Mathematik'' (Germany, 1985--).

icon-balldong.gif (1653 bytes)Beijing Math. Society (Vice-Director) (1996--).

icon-balldong.gif (1653 bytes)Vice-Chief  Editor of "Mathematics in Practice and Theory" (1997-)

icon-balldong.gif (1653 bytes)Editor of "World Science and Technology-Research & Development" (1995--)

icon-balldong.gif (1653 bytes)Chairman of Committee of Math Academic Degree, Tsinghua Univ.(1997-2000)

icon-balldong.gif (1653 bytes)Commissioner of Committee of Academic Degree, Tsinghua Univ.(1997-2000)
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earthanim1.gif (52377 bytes)ACADEMIC TALKS:   

Centennial of American Math. Society, Providence, USA, 1988;

Meeting 843 of American Math. Society, Maryland, USA, 1988 ;

International Congress of Mathematicians, Zurich, Switzerland, (short communication)1994;

National Congress on Number Theory II & III, Hefei 1983; Chengdu 1991;

University of New York City, USA, 1988;

University of Maryland, USA, 1987;

University of Rome, Sapienza, Italy, 1992;

University of Trieste, Italy, 1992;

ETH, Swiss Federal Institute of Technology, Zurich, Switzerland, 1992;

ICTP, International Centre for Theoretical Physics, Italy, 1992 ;

National Summer School of Mathematical Graduate-Students ,Beijing, 1996;

Chongqing University, Sichuan, 1991;

Information Institute of The Army, 1992.

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earthanimsmallb.gif (21878 bytes)Writing Comments of

Prof.      Don Zagier

and    L. C. Washington :

 

ZHANG  is

``among  China's  leading   number  theorists  today ''

[1989.1.5,Maryland USA];

TO THESIS: ``these papers would without any question

earn Mr. Zhang a doctorate in any university of Europe

or the United States.   I recommend him highly ''

[1984.2.2,Bonn].

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PUBLICATIONS

(in chronological order):

[1] Research on Several Abelian Number Fields, Thesis of B.Sc. Degree, Univ. of Science  and Technology of China, 1981.

[2] On Four Types of Algebraic Number Fields and Algebraic Function Fields, PH. Doctorate Dissertation, Univ. of Science and Technology of China, 1985; "A Collection of Ph. D. Dissertations", Vol. 2(Science), published by Univ. Sci. Tech. China, 1988, pp. 39-108.

[3] Analysis of the Behaviour of Error-detecting Codes Under Conditions of Feedback and Retransmission Error Control, Acta Math. Applagatae Sinica, 2(1979), No. 3, 278- 286; Math. Rev. 81j: 94029. (cooperated with Feng Keqin).

[4] On Number Fields of Type (2, 2, ... , 2) , J. China Univ. Sci. Tech., 12 (1982), No.4, 29-41; Math. Rev. 84j: 12007.

[5] Density of Discriminants of Fields of Type (2, 2, ... , 2), Kexue Tongbao (Monthly J. Scien.), 28(1983), No. 12, 1708; Math. Rev. 86d: 11096.

       (Its Chinese Version , Kexue Tongbao(Chinese), 27 (1982), No. 21, 1342.)

[6] On Relative Integral Bases of Quartic Cyclic Number Fields, Kexue Tongbao (Monthly J. Scien.), 28(1983), No. 4, 456-457; Math. Rev. 85e: 11081; Zentral. Math. 513.12004 (cooperated with Feng Keqin).

      (Its Chinese Version , Kexue Tongbao, 27(1982), No.16, 961 ).

[7] On Number Fields of Type (L, L, ... , L) , Scientia Sinica, A27(1984), No. 10, 1018-1026; Math. Rev. 86j: 11106; Zentral. Math. 616(1987), 12001.

       (Its Chinese Version, Scientia Sinica (Chinese), A1(1984), 31-38. )

[8] Density of Number Fields of Type (2, 2, ... , 2), Scientia Sinica, A27(1984), No.4, 345-351; Math. Rev. 86d: 11096.

       ( Chinese Version, Scientia Sinica(Chinese), A9(1983), 805-811. )

[9] Relative Integral Bases of Cyclic Quartic Fields(in Chinese), Acta Math. Sinica, 27(1984), No.3, 425-432;

    Math. Rev. 87c: 11102; Zentral. Math. 537(1985), 12005.

[10] Note on a Paper : "The Integers of Normal Quartic Fields" [Ann. of Math. (2) 31(1930), 381- 418;

      Jbuch 56, 870] by A. A. Albert, J. China Univ. Sci. Tech., 14(1984), No. 2, 171-177; Math. Rev. 86b: 11066.

[11] Cyclic Quartic Fields and Genus Theory of Their Subfields, J. Number Theory, 18 (1984), No.3, 350-355;

        Math. Reviews 85k: 11053; Zentral. Math. 546.12002.

[12] Note on a Paper by A. A. Albert, Monthly Journal of Science (Kexue Tongbao), 29 (1984), No.11, 1434-1435;   

        Math. Rev. 86k: 11058.

        (Chinese Version, Kexue Tongbao (Chinese), 29(1984), No.13, 776-777. )

[13] Relative Integral Bases and Units of C_L^n Fields, J. China Univ. Sci. Tech., 14(1984), No. 3, 427-428.

[14] A Simple Construction of Genus Fields of Abelian Number Fields, Proceed. of American Math. Soc. 94(1985),

         No.3. 393-395; Math. Reviews 86h: 11091.

[15] Relative Integral Bases and Units of Fields of Type (L, L, ... , L) (in Chinese), Acta Math. Sinica, 29(1986),

         No. 5, 622-627; Math. Rev. 88d: 11100 .

[16] Counterexample and Correction About Genus Fields of Number Fields, J. of Number Theory, 23(1986), No.3, 318-321; Math. Rev. 88c: 11065.

[17] Arithmetic of n-quadratic Algebraic Function Fields, Monthly Journal of Science (Kexue Tongbao), 32 (1987), No.17, 1157-1161.

      ( Chinese Version , Kexue Tongbao (in Chinese), 31 (1986), No.16, 1201-1204 . )

[18] Congruences of Class Numbers of General Cyclic Cubic Number Fields, J. China Univ. Sci. Tech. 17 (1987), No. 2, 141-145; Math. Rev. 88i: 11076.

[19] Congruences for Class Numbers of General Cyclic Quartic Fields, Chinese Science Bulletin, 33 (1988), No.22, 1145-1148 ; Math. Rev. 89g: 11101.


       (Chinese Version, Kexue Tongbao (in Chinese), 32(1987), No. 23, 1761-1763 . )

[20] Ambiguous Classes and 2-ranks of Class Groups of Quadratic Function Fields, J. China Univ. Scien. Tech. 17(1987), No.4, 425-430; Math. Rev. 89j: 11115 .

[21] Algebraic Function Fields of Type (2, 2, ... , 2) , Scientia Sinica, Series A31(1988), No. 5, 521-530; Math. Rev. 90a: 11143.

         (Chinese Versin, Scientia Sinica (in Chinese), Series A1(1988), 8-16. )

[22] Determination of Algebraic Function Fields of Type ( 2, 2, ... , 2) with Class Number One, Scientia Sinica, A31(1988), No.8, 908-915; Math. Rev. 90a: 11144.

         (Chinese Version, Scientia Sinica (in Chinese), A 2(1988), 129-135. )

[23] Seven Topics on Methodology of Academic Studying and Research, J. for Students of Univ. Scien. Tech. China, 4(1988), 71-81; also in <>, Ji Chen & Zhonghao Ye ed., Front of Element. Math.,  Jiangsu Education Press, Vol. 1, 1995, pp.399-416.

[24] Congruences of Class Numbers of Number Fields, American Math. Soc. Meeting 843, Maryland, April 1988.

[25] Ten Formulae of Type Ankeny-Artin-Chowla for Class Numbers of General Cyclic Quartic Fields, Scientia Sinica, A 32(1989), No.4 ,417-428; Math. Rev. 91b: 11112.

        (Chinese Version, Scientia Sinica ( in Chinese), A7(1988), No.7, 688-697. )

[26] Class Numbers and Units of Several Kinds of Quadratic Fields , presented at the Centennial of Amer. Math. Soc. (AMS Meeting. 844), Providence, August 1988; Abstract. of Amer. Math. Soc. (1988.8).

[27] Congruences Modulo 8 for Class Numbers of General Quadratic Fields Q(\sqrt m ) and Q(\sqrt -m ), J. Number Theory, 32(1989), No.3, 332-337; also presented at Amer. Math. Soc. Meeting 843, 1988 ; Math. Rev. 90k: 11137.

[28] Solutions of the Diophantine Equations Related to Real Quadratic Fields, Chinese Science Bulletin, 37(1992), No.11, 885-889; Zentral. Math. 762.11036.

       ( Chinese Version, Kexue Tongbao( in Chinese), 36(1991), No. 23, 1772-1775. )

[29] The Determination of Subgroups in Ideal Class Groups of Real Quadratic Fields, Chinese Science Bulletin, 37(1992), No.11: 890-893; Zentral. Math. 762.11037.

        (Chinese Version, Kexue Tongbao, (Chinese), 36(1991), No.24: 1847-1849. )

[30] Determination of Solutions and Solvabilities of Diophantine Equations and Quadratic Fields, "Algebraic Geometry and Algebraic Number Theory", World Science, Singapore/London, Vol.3 (1992), 189-199

[31] Criteria of Class Number h(K)=1 for Real Quadratic Fields, Chinese Science Bulletin, 38 (1993), No. 4, 273-276; Zentral. Math. 773.11060.

         (Chinese Version, Kexue Tongbao (in Chinese), 37(1992), No. 11, 2017-2019. )

[32] Class Groups of Certain Real Quadratic Fields, J. China Univ. Scien. Tech. 22(1922), No. 4, 393-395.

[33] Relative Integral Basis of Fields of Type (q^s, q^s, ..., q^s), Chinese Science Bulletin, 38 (1993) , No. 16, 1336-1339.

       (Chinese Version , Kexue Tongbao (in Chinese) , 38(1993), No. 9, 777-779. )

[34] Class Group H(d) and Class Number h(d) of Q(\sqrt d) and Cohen-Lenstra Heuristics and Diophantine Equations, ICM 94, Intern. Congress of Mathematicians, Zurich, August, 1994 (cooperated with L. C. Washington); (short communication) Abstract of ICM 94.

[35] Equations of Real Quadratic Fields and Semi-Simple and Continued Fractions, Chinese Science Bulletin, 40(1995), No. 21, 1761-1765.

       (Chinese Version , Kexue Tongbao (in Chinese), 40(1995), No. 10, 865-867. )

[36] Some Composite Relative Extensions and Relative Integral Bases, Algebraic Colloquium, 2(1995), No. 3, 269-274.

[37] New Development of Fermat's Last Theorem, World Scientific Research and Development, 17 (1995), No. 4, 26-27 .

           (Continuing in the following "Recent Publications")                           

RECENT   PUBLICATIONS

[38] Existence of Integral Bases for Relative Extensions of N-Cyclic Number Fields,

      J. Number Theory, 60(1996.10), No. 2, 409416.

[39] Ideal Class Groups of Real Quadratic Fields of Generalized ERD-Type,

      Tsinghua Science and Technology, 1(996), No. 3, 263-265.

[40] Relative Integral Bases of Abelian q-fields, Chinese Science Bulletin, 41(1996),

        No. 13, 1065-1068.  

              (Chinese version: Kexue Tongbao, 41(1996.6), No. 12, 1066-1068)

[41] Cllasification and Prime Decomposition of Abelian q-fields, Chinese Science

          Bulletin, 41(1996), No.24, 2025-2028.

       (Chinese version: Kexue Tongbao,  41(996.12), No. 23, 2113-2115).

[42] Ideal Class Groiups and Their Subgrouips of Real Quadratic Fields, (with

       Prof. L.C. Washington), Science in China, Seies A 40(1997), No.9, 909-916.

            (Chinese version:    A27(1997), No. 6: 522-528).

[43] Modification of Cohen-Lenstra Heuristics for Ideal Class Groiups and Numbers

       of Certiain Real Quadratic Fields, (With L.C. Washington), Chinese Science

       Bulettin, 42(1997), No.23, 1959-1962.

            (Chinese version: 42(1997.10), No. 19: 2053-2056

[44] Fermat's Last Theorem -- Proof of A. Wiles, World Sci. Tech. Research and

       Development, 19(1997), NO.1, 74-78 (in Chinese).

[45] Heuristics and  Related Results on Class Groups of Real Quadratic Fields,

       (with L. C. Washington), Science in China, A41(1998), No.4. 365-370.

          (Chinese version:      A28(1998), No. 2: 140-144).

[46].  Advanced Algebra, Tsinghua Univ. Press, 1998.3, Beijing

        (in Chinese)

[47] Intro. to   Algebraic Number Theory, Hunan Edu. Pub.,

1999.1, China  (authorized by  National Dept of  Education as "Graduate Texts of

China" )

[48] Structure and Prime Decomposition Law and Relative Extensions of Abelian

         Fields with Prime Power Degree, Science in China, A42(1999), No.8, 816-824

         (Chinese version: A29(1999), No.6, 509-517)

[49]  Explicit Classification for the Torsion Cyclic Subgroups of Rational Points with

     Even Order of Elliptic Curves, Chinese Science Bulletin, 44(1999), No.21, 1951-1952

        (Chinese version: 44(1999),      No.11, 1152-1154)

[50] Explicit Determination of Torsion Subgroup of Elliptic Curves over Multi-

      Quadratic Fields, with Qiu Derong, Advances in Math., 28(1999), No.5, 475-478

[51] Steinitz Class of Mordel-Weill Groups of Elliptic Curves with Complex Multipli-

     cation (with Tong Liu), Pacific Journal of Mathematics, 193(2000), No.2, 371-379.

    (This paper is available via http://nyjm.albany.edu:8000/PacJ/2000/193-2-7.html )

[52] Fundamental Unit System and Class Number for Real Number Fields of Type

   (2, 2, 2), with Wang Kunpeng, Tsinghua Science and Technology, 5(2000), 2:150-153.

[53] The Fundamental Units of Algebraic Real Quadratic Function Fields, with

          Wang Kunpeng, Advances in Math., 29(2000), No.2, 179-180.

[54] Elliptic Curves of Twin-Primes over Gauss Field and Diophantine Equation,

            with Qiu Derong, Advances in Math. 29(2000), No.3, 279-281.

[55]. Steinitz Class of Elliptic Curves with Complex Multiplication (with Liu Tong),

         Progress in Natural Science, 10(2000), No.4, 310-313.

[56]  Elliptic Curves and Their Torsion Groups over Number Fields of Type

              (2, , 2) ,    with Qiu Derong,  Science in China,  A44 (2001.2), 2:159-167

               (Chinese version:     A30(2000),   No.7, 612-619.)

[57] Continued fraction of functions connected with real quadratic function fields, with Wang Kunpeng, Advanced in Math. 29(2000. 8), No.4, 375-377.

[58]   Selmer groups and Mordell-Weil groups of two types of elliptic curves, with Qiu Derong, Progress in Natural Science, 10(2000.12), No.12, 946-949

[59]   Ideal class groups and subgroups of real quadratic function fields, with Wang Kunpeng, Tsinghua Science and Technology, 5(2000.12), No.4: 372-373

[60]   Lower bound for ideal class numbers of real quadratic function fields, with Wang Kunpeng, Tsinghua Science and Technology, 5(2000.12), No.4: 370-371

[61]   Elliptic Curves and Their Torsion Subgroups Over Number Fields of Type (2, 2, , 2), with Qiu Derong, Science in China, A44, 2(2001), 159-167. (IDS Number: 406BV)

[62]  Special values of L-series attached to two families of CM elliptic curves, with Qiu Derong, Progress in Natural Sciences, Vol.11(2001), 11, 865-870(IDS Number: 488VG)

[63] Explicit Classification for Torsion Subgroups of Rational Points of Elliptic Curves ,by Rong QIU, Xian Ke ZHANG, Acta Mathematica Sinica (English Series), 18(2002.7), No.3, 539-548 (IDS Number: 579MC)

 

[64] L-Series and Their 2-adic Valuations at s=1 Attached toCM Elliptic Curves,by Derong Qiu and  Xianke Zhang, Acta Arithmetica, 103.1(2002), 79-95 (IDS Number:613VP)

[65]   Explicit Formulae for Values of Dedekind Zeta Functions of Two Kinds of Cyclotomic Fields, by Ma Lianrong and Zhang Xianke, Advances in Math., 31(2002.2), No.1, 90-92)

[66] Mordell-Weil Groups and Selmer Groups of Twin- Prime Elliptic Curves, by Qiu Derong and  Zhang Xianke, Science In China, A45(2002.11), No.11, 1372-1380(IDS Number:614UL)

[67] Elliptic Curves with CM by  and 3-adicvaluations of their L-series,by Qiu Derong and Zhang Xianke, Manuscripta Math. 108, 385-397 (2002)( IDS Number: 586YB)

[70] Subgroups of Ideal Class Groups of  Real Quadratic Algebraic Function Fields, by Wang Kunpeng and Zhang Xianke, Science in China (Series A), Vol.46(2003), No.3, 339-345(IDS Number:698FC)

 

[71] Subgroups of Class Groups of Algebraic Quadratic Function Fields, by Wangkunpeng and Zhang Xianke, Chin. Ann. Math., 24B:3(2003), 315-322

 

[72] Unit Group of Algebraic Real Quadratic Function Fields, by Wang Kunpeng and Zhang Xianke, J. of Graduate School of the Chinese Academy of Sciences, 20(2003-6), No.2, 139-145.

         

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