Tao Zhan（展涛）
Curriculum Vitae
Family name and given nameFamily 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.
