ZHAN TAO

INDEX

• Address
• Education
• Overseas Research
• Research Interest
• Positions
• Publications
• Delivered Talks
• Back to Mainpage

Current Address

Tao ZHAN, Ph.D
Professor
Department of Mathematics
Shandong University
250100 Jinan, Shandong
PR CHINA
Tel: ++86/531/8906961 with extension 2953
Fax: ++86/531/8902167
Email: zhantao@sdu.edu.cn

Education

• B.S: Shandong University (1983)
• M.S: Shandong University (1995), Supervisor: Professor Chengdong PAN
• Ph.D: Shandong University (1987), Supervisor: Professor Chengdong PAN

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.

Research Interests

• Goldbach conjecture and other additive problems;
• Exponential sums over prime variables;
• Bombieri-Vinogradov type mean value theoreoms;
• Riemann Zeta function and Dirichlet L-function.

Positions

• Vice-President of Shandong University
• Chairman of Shandong Mathematics Society
• Member of the Standing Committee of All China Youth Association

Selected Publications

1. On the Distribution of K-full Integers
   Science in China(A), vol.32 (1989), 20-37.
2. On the Distribution of K-full Integers II
   Chin. Adv. Math., vol.17, No.1(1988), 94-96.
3. On the Error Function of Square-full Integers
   Chin. Ann. Math.(Ser B), vol.10, No.2(1989), 227-235.
4. Bombieri's Theorem in Short Intervals
   Acta Math. Sinica (New Series), vol.5, No.1(1989), 37-47.
5. On the Representation of Large Odd Integers as Sum of Three Almost Equal Primes
   Acta Math. Sinica (New Series), vol.7, No.3(1991), 259-272.
6. Davenport's Theorem in Short Intervals
   Chin. Ann. Math.(Ser B),vol.12, No.4(1991), 421-431.
7. On the Mean Square of Dirichlet L-functions
   Acta Math. Sinica (New Series), vol.8, No.2(1992), 204-224.
8. On the Distribution of Integers with a Fixed Number of Prime Factors
   Math. Z., vol.213 (1993), 133-147 (joint with Dieter Wolke).
9. Some Remarks on the Binary Goldbach Problem
   Arch. Math., vol.16 (1993), 241-249 (joint with Dieter Wolke).
10. A Generalization of the Goldbach-Vinogradov Theorem
    Acta Arith., vol.71 (1995), 95-106.
11. A Generalization of Bombieri's Theorem and Its Applications
    Science in China (Series A), vol. 38, No.12 (1995), 1432-1443 (joint with Jiafa Lin).
12. Some Almost-all Results concerning the Sapiro Primes
    Chin. Ann. Math.(Ser B), vol.17, No.3 (1996), 279-288 (joint with Dietmar Fischer).
13. On Sum of Five Almost Equal Prime Squares
    Acta Arith., vol.77 (1996), 369-383 (joint with Jianya Liu).
14. Exponential Sums involving the Mobius Function
    Indag. Mathem., New Series, vol.7, No.2 (1996), 271-278 (joint with Jianya Liu).
15. A Bombieri Type Theorem of Exponential Sums with Prime Variable
    Chin. Sci. Bull., vol.41, No.3 (1996), 193-195 (joint with Jianya Liu).
16. Estimation of Exponential Sums over Primes in Short Intervals II
    Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, edited by B.C. Berndt, H.G. Diamond & A.J. Hildebrand, 571-606, Birkhauser 1996 (joint with Jianya Liu).
17. The Ternary Goldbach Problem in Arithmetic Progressions
    Acta Arith., vol.82, No.3(1997), 197-227 (joint with Jianya Liu).
18. Estimation of Exponential Sums over Primes in Short Intervals I
    Monatash. Math.(accepted, joint with Jianya Liu).
19. The Goldbach Problem with Primes in Arithmetic Progressions
    London Math. Soc. Lecture Notes 247, Analytic Number Theory, edited by Yoichi Motohashi, Cambridge University Press, 1997 , 227-251 (joint with Ming-Chit Liu)
20. On a Theorem of Hua
    Arch. Math., vol.69(1997),375-390 (joint with Jianya Liu).
21. On Sum of Five Almost Equal Prime Squares
    Science in China (accepted, joint with Jianya Liu).

Talks Delivered at International Conferences

1. The Goldbach-Vinogradov Theorem in Short Intervals
   International Conference in Number Theory, Oberwohlfach 1991.
2. Some Remarks on the Binary Goldbach Problem
   International Conference in Number Theory, Marseille, Luminy 1992.
3. On Integers with a Fixed Number of Prime Factors
   Annual Meeting of the Germany Mathematics Society, Berlin 1992.
4. On the Distribution of a special Class of Integers
   International Conference in Number Theory, Hong Kong 1993.
5. Estimation of Non-linear Exponential Sums over Primes
   International Conference in Number Theory in Honor of Professor Heini Halberstam, Urbana-Champaign 1995.
6. The Goldbach Problem with Primes in Arithmetic Progressions
   International Conference in Number Theory, Kyoto 1996.
7. On Some Problems in the Additive Prime Number Theory
   Workshop and Conference in Number Theory, Hong Kong 1996.
8. On Sum of Prime Squares
   International Conference in Number Theory in Honor of Professor Andrej Schinzel, Zakopane, Poland 1997.
9. The Goldbach-Vinogradov Theorem with Restrictions on Prime Variables
   101 Years of Prime Number Theorem, Ulm, Germany 1997.