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Tao ZhanչΣ

Curriculum Vitae

Family name and given name

Family name: Zhan; given name: Tao

 

Address

School of Mathematics
Shandong University
Jinan, Shandong 250100
P. R. China
Email: zhantao(at)sdu.edu.cn

 

Education

Ph.D.: Shandong University, 1987
M.S.:   Shandong University, 1985
B.S.:   Shandong University, 1983

 

Professional Positions

2008- 2011:   Professor, Jilin University
Feb-July 1996:  Research Fellow, The University of Hong Kong,
                         supported by the Croucher Foundation
1991-1992:       Research Fellow, University of Freiburg, Germany,
                         supported by the Alexander von Humboldt Foundation
1991-present:   Professor, Shandong University
1989-1991:       Associate Professor, Shandong University

Special Functions

Member of Editorial Board of Acta Mathematica Sinica
2008- 2011:                 President, Jilin University;
2000-2008:                 Chairman, Shandong Mathematical Society
2000-2007:                 Standing syndic, Chinese Mathematical Society
Jul. 2000-Nov. 2008:   President, Shandong University;
Mar. 1995-Jun. 2000:  Vice-president, Shandong University
Apr. 1993-Feb. 1995:  Vice-dean, School of Mathematics, Shandong University

Research Interests

Additive theory of prime numbers
Exponential sums over prime variables
Bombieri-Vinogradov type mean value theoreoms
Riemann Zeta function and Dirichlet L-functions

 

Grants

2006-2008: Key project "the arithmetic and geometry of automorphic forms", by                    the National Natural Science Foundation
2005-2007: Major grant program for sciences and technology, by the Ministry of                    Education

 

Overseas Research Experience

1991-1992: Institute of Mathematics, University of Freiburg in Germany
                   Research Fellow supported by the Alexander von Humboldt                    Foundation in Germany.
Feb-July 1996: Department of Mathematics, The University of Hong Kong                         Research Fellow supported by the Croucher Foundation in                         Hong Kong.

 

Publications

[31] (with J.Y. Liu) The quadratic Waring-Goldbach problem, J. Shandong        University, 42(2) (2007), 1-18.
[30] (with J.Y. Liu and G.lv) Exponential sums over primes in short intervals. Sci.        China Ser. A49 (2006), no. 5, 611--619.
[29] (with J.Y. Liu) The exceptional set in Hua's theorem for three squares of        primes. Acta Math. Sin. (Engl. Ser.)21 (2005), no. 2, 335--350.
[28] (with J.Y. Liu and M.C. Liu) Squares of primes and powers of 2. II, J. Number        Theory 92 (2002), no. 1, 99-116.
[27] (with J.Y. Liu) Distribution of integers that are sums of three squares of        primes, Acta Arith. 98 (2001), no. 3, 207-228.
[26] (with C. Bauer and M.C. Liu) On a sum of three prime squares, J. Number        Theory 85 (2000), no. 2, 336-359.
[25] (with J.Y. Liu) Hua's theorem on prime squares in short intervals, Acta Math.        Sin. (Engl. Ser.) 16 (2000), no. 4, 669-690.
[24] (with J.Y. Liu and M.C. Liu) Squares of primes and powers of $2$, Monatsh.       Math. 128 (1999), no. 4, 283-313.
[23] (with J.Y. Liu) Estimation of exponential sums over primes in short intervals. I,       Monatsh. Math. 127 (1999), no. 1, 27-41.
[22] (with J.Y. Liu) Sums of five almost equal prime squares. II, Sci. China Ser. A 41       (1998), no. 7, 710-722.
[21] (with J.Y. Liu ) The Goldbach-Vinogradov theorem, Number theory in       progress, Vol. 2 (Zakopane-Ko\'scielisko, 1997), 1005-1023, de Gruyter,       Berlin, 1999.
[20] (with J.Y. Liu ) On a theorem of Hua, Arch. Math. (Basel) 69 (1997), no. 5,       375-390.
[19] (with M.C. Liu) The Goldbach problem with primes in arithmetic progressions,      Analytic number theory (Kyoto, 1996), 227-251, London Math.Soc, Lecture      Note Ser., 247, CambridgeUniv. Press, Cambridge, 1997.
[18] (with J.Y. Liu ) The ternary Goldbach problem in arithmetic progressions, Acta       Arith. 82 (1997), no. 3, 197-227.
[17] (with J.Y. Liu) Exponential sums involving the Mö bius function, Indag.       Math. (N.S.) 7 (1996), no. 2, 271-278.
[16] (with J.Y. Liu ) A Bombieri-type mean-value theorem concerning exponential       sums over primes, Chinese Sci. Bull. 41 (1996), no. 5, 363-366.
[15] (with J.Y. Liu ) On sums of five almost equal prime squares, Acta Arith. 77       (1996), no. 4, 369-383.
[14] (with D. Fischer) Some almost all results concerning the Pjateckii-Sapiro prime       numbers, A Chinese summary appears in Chinese Ann. Math. Ser. A 17       (1996), no. 4, 515, Chinese Ann. Math. Ser. B 17 (1996), no. 3, 279-288.
[13] (with J.Y. Liu ) A Bombieri-type mean value theorem for prime variable        trigonometric sums, (Chinese) Kexue Tongbao (Chinese) 41 (1996), no. 3,        193-195.
[12] (with J.Y. Liu ) Estimation of exponential sums over primes in short intervals. II,       Analytic number theory, Vol. 2 (Allerton Park, IL, 1995), 571-606,
      Progr. Math., 39,Birkhäuser Boston, Boston, MA, 1996.
[11] (with J.F. Lin) Generalization of Bombieri's theorem and its applications,
      Sci. China Ser. A 38 (1995), no. 12, 1432-1443.
[10] A generalization of the Goldbach-Vinogradov theorem, Acta Arith. 71 (1995),       no. 2, 95-106.
[9] (with D. Wolke) Some remarks on the binary Goldbach problem, Arch. Math.       (Basel) 61 (1993), no. 3, 241-249.
[8] (with D. Wolke) On the distribution of integers with a fixed number of prime       factors, Math. Z. 213 (1993), no. 1, 133-144.
[7] On the mean square of Dirichlet $L$-functions, A Chinese summary appears in      Acta Math. Sinica 36 (1993), no. 3, 432, Acta Math. Sinica (N.S.) 8 (1992), no.      2, 204-224.
[6] Davenport's theorem in short intervals, A Chinese summary appears in      Chinese Ann. Math. Ser. A 12 (1991), no. 5, 644, Chinese Ann. Math.Ser. B 12      (1991), no. 4, 421-431.
[5] On the representation of large odd integer as a sum of three almost equal      primes, A Chinese summary appears in Acta Math. Sinica 35 (1992), no. 4,      575, Acta Math. Sinica (N.S.) 7 (1991), no. 3, 259-272.
[4] Distribution of $k$-full integers, Sci. China Ser. A 32 (1989), no. 1, 20-37.
[3] On the error function of the square-full integers, A Chinese summary appears      in Chinese Ann. Math. Ser. A 10 (1989), no. 3, 388, Chinese Ann. Math. Ser. B      10 (1989), no. 2, 227-235.
[2] Bombieri's thoerem in short intervals, A Chinese summary appears in Acta      Math. Scinica 33 (1989), no. 2, 287, Acta Math. Sinica (N.S.) 5 (1989), no. 1,      37-47.
[1] On a theorem of Darvenport [Davenport], Chinese Quart. J. Math. 2 (1987), no.      2, 52-58.

 

Invited Talks

[9].The Goldbach-Vinogradov Theorem with Restrictions on Prime Variables, 101      Years of Prime Number Theorem, Ulm, Germany 1997.

[8].On Sum of Prime Squares, International Conference in Number Theory in       Honor of Professor Andrej Schinzel, Zakopane, Poland 1997.

[7].On Some Problems in the Additive Prime Number Theory, Workshop and      Conference in Number Theory, Hong Kong 1996.

[6].The Goldbach Problem with Primes in Arithmetic Progressions, International       Conference in Number Theory, Kyoto 1996.

[5].Estimation of Non-linear Exponential Sums over Primes, International      Conference in Number Theory in Honor of Professor Heini Halberstam,      Urbana-Champaign 1995.

[4].On the Distribution of a special Class of Integers, International Conference in      Number Theory, Hong Kong 1993.

[3].On Integers with a Fixed Number of Prime Factors, Annual Meeting of the      Germany Mathematics Society, Berlin 1992.

[2].Some Remarks on the Binary Goldbach Problem, International Conference in      Number Theory, Marseille, Luminy 1992.

[1].The Goldbach-Vinogradov Theorem in Short Intervals, International       Conference in Number Theory, Oberwohlfach 1991.

 

 
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