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CURRICULUM
VITAE of
Address : Tsinghua University, Department
of Mathematical Sciences,
Beijing
100084, P. R. China
 UNIVERSITY
EDUCATION
RESEARCH
PRIZES AND AWARDS
MEMBERSHIP AND SERVICE
ACADEMIC TALKS
Writing Comments
Recent Publications 
Publ.-list in《Math. Reviews》(partial)
Reviews by 《Math. Reviews》(partial)
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.
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
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.
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)
 International Center for
Theoretical Physics (Regular Associate Member(1991--),
Senior A. Member (1999--).
American Mathematical
Society (1985--).
Regular Reviewer of
``Mathematical Reviews'' (USA) (1985--).
Regular Reviewer of
``Zentralblatt fur Mathematik'' (Germany, 1985--).
 Beijing Math. Society (Vice-Director)
(1996--).
Vice-Chief Editor
of "Mathematics in Practice and Theory" (1997-)
Editor of "World
Science and Technology-Research & Development" (1995--)
Chairman of Committee of
Math Academic Degree, Tsinghua Univ.(1997-2000)
Commissioner of Committee
of Academic Degree, Tsinghua Univ.(1997-2000)
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.
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].
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, 409—416.
[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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