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Today is ：
Dept.
of Mathematical Sciences , Tsinghua
University, Beijing
100084 , P. R. China
Associate
Member of "International Centre for Theoretical Physics" (UNESCO,
Italy)
Academic
Areas: Number Theory, Algebra, Algebraic Function Theory, Elliptic
Curves.
 Recent Publications  
 PRIZES AND AWARDS
MEMBERSHIP
AND SERVICE
ACADEMIC
TALKS
Writing Comment
PUBLICATIONS
RECENT PUBLICATIONS
Papers
reviewed by《Mathematical Reviews》 (Partial)
Reviewes
by《Mathematical
Reviews》 (Partial)
Email(O) :
Email(H): master@tsinghua.edu.cn
URL:
http://faculty.math.tsinghua.edu.cn/faculty/~xzhang/
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 PRIZES &
AWARDS
I. "Ph. Doctor of China Having Outstanding
Merit''
(by State
Education Commission & State Academic-Degree
Commission, January 1991).
II. National Natural-Science Prize (1990, with K.
Feng and H. Lu).
III. Scientific Progress Prize (Academia
Sinica, 1988, with Feng & Lu).
IV. Prize of Scientific Treatise (Anhui Province,
1986).
V. Prize of Scientific Research (Univ. Sci. Tech.
China, 1985).
VI. Prize of "Good Teacher and Helpful Friend
of Graduate-Students" (Tsinghua Univ., 1998).
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 MEMBERSHIP
AND SERVICE
 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)
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ACADEMIC TALKS
Centennial of
American Mathematical Society, Providence, USA, 1988;
Meeting 843 of
American Mathematical Society, Maryland, USA, 1988 ;
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, 1994, 1997;
National Summer
School of Mathematical Graduate-Students, Beijing, 1996;
Information
Institute of The Army, 1992.
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Writing Comments of
Prof. Don B.
Zagier
& L. C. Washington:
Zhang is
``among China's leading number theorists today ''
[1989.1.5, Maryland USA];
To thesis in 1983: ``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, 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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URL: http://faculty.math.tsinghua.edu.cn/faculty/~xzhang/
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