Address

School of Mathematical Sciences,

Shandong Normal University,

Jinan 250014, Shandong,

P. R. China

Tel: 0531-86182506

E-mail: zhaiwg@hotmail.com, wgzhai@163.com

Education

B.S.:  Shandong University, 1991

Ph.D.: Shandong University, 1996

Professional Positions

1996.9-1997.11,  Lecturer ,  Shandong Normal University

1997.11-1999.11,  Associate Professor,  Shandong Normal University

1999.11-present,  Professor,  Shandong Normal University

2001.10-2003.9,  Post-doctoral fellow,  Nagoya University

Conferences

1999.9,   The first China-Japan number theory seminar, Beijing

2001.11,  Analytic number theory seminar of Kyoto University, Kyoto

2002.10,  Analytic number theory seminar of Kyoto University, Kyoto

2004.2,   The third China-Japan number theory seminar, Xi’an

2004.12,  ICCM 2004,   Hongkong                                 

2006.8,  The fourth China-Japan number theory seminar, Weihai

Research Interests

Multiplicative number theory, Exponential sum，Lattice points problem

Grants

2004-2006: Natural Science Foundation of China(Grant No. 10301018)

1998-2001: Natural Science Foundation of Shandong Province

Preprints

[1] (with Y. Tanigawa and D. Y. Zhang) On the Rankin-Selberg problem: higher power moments of the Riesz mean error term, to appear in Science in China (Series A)

Publications

[42] (with X. D. Cao)On a Diophantine inequality over primes(II), Monatsh.  Math. ，2007，Vol. 150, 173-179.

[41] Renyi’s problem in short intervals, Acta Mathmetica Sinica，2007，Vol.23(1), 29-36.

[40] (with Y. Tanigawa) Dirichlet series associated with polynomials and applications, J. of Number Theory 122(2007), 466-518.  

[39] (with D. Y. Zhang) On the difference of two coprime cubes(in Chinese), Acta Math. Sinica, Vol. 49(5), 1181-1188.

[38] On higher power moments of $\Delta(x)$.IV(in Chinese), Acta Math. Sinica, Vol. 49(5), 639-646.

[37] (with D. Y. Zhang) On integers $n$ coprimes to $[n^c]$ (in Chinese), Acta Math. Sinica, Vol. 49(2), 469-472.

[36] (with  D. Y. Zhang) On the maximal $k-$ factor(in Chinese), Acta Math. Sinica, 2006，Vol. 49(1), 205-214.

[35] (with D. Y. Zhang) On the Waring-Goldbach problem in thin subsets of primes(in Chinese), Acta Math. Sinica, 2005，Vol. 48(4)，809-816.

[34] Square-free numbers as sums of two squares, Number Theory: Tradition and Modernization, pp. 219-227，2006.

[33] On the mean value of composition of an integer, Acta Arith., 2006, Vol. 125(4), 331-345.

[32] (with J. Furuya) On the k-free divisor problem, Acta Arith., 2006，Vol. 123(3), 267-287.

[31] (with  X. D. Cao)On sums of two coprime k-th powers(II), Monatsh. Math. 148(2006), 153-172.

[30] On sums of two coprime k-th powers, Monatsh. Math. 144(2005), 233-250.

[29] On higher-power moments of $\Delta(x)$. III, Acta Arith. 118 (2005),263-281.

[28] On higher-power moments of $E(t)$. Acta Arith. 115 (2004), no. 4, 329--348.  

[27] On higher-power moments of $\Delta(x)$. II. Acta Arith. 114 (2004), no. 1, 35--54.

[26] On higher-power moments of $\Delta (x)$. Acta Arith. 112 (2004), no. 4, 367--395.

[25] (with G. S. Lv) On three-dimensional divisor problem of (a,a,b) type(in Chinese)       Advances in Mathematics, 33(2004), 195-202.
[24] (with G. S. Lv)The divisor problem on the Beatty sequence(in Chinese), Acta Math. Sin.,      47(2004), 1213-1216.

[23](with  X. D. Cao) On a binary Diophantine inequality. Adv. Math. (China) 32 (2003), no. 6, 706--721.  

[22] Short interval results for a class of integers. Monatsh. Math. 140 (2003), no. 3, 233--257.  

[21] (with  X. D. Cao) On a Diophantine inequality over primes. Adv. Math. (China) 32 (2003), no. 1, 63--73.  

[20] On primitive lattice points in planar domains. Acta Arith. 109 (2003), no. 1, 1--26. 

[19] (with G. S. Lv) On the sum of multi-dimensional divisor function on a special      sequence(in Chinese),  Advances in Mathematics, 32(2003), 660-664.
[18] (with G. S. Lv)A special two-dimensional divisor problem(in Chinese), Pure and       Applied Mathematics, 18(2002), 348-352.
[17] (with G. S. Lv)A special divisor problem(in Chinese), Acta Math. Sin., 45(2002),  991-1004.

[16] On the number of primitive Pythagorean triangles. Acta Arith. 105 (2002), no. 4, 387--403.  

[15] (with  X. D. Cao)  On systems of Diophantine inequalities and equations with prime numbers. Adv. Math. (China) 31 (2002), no. 3, 243--248.  

[14] On the simultaneous distribution of the fractional parts of different powers of prime numbers. J. Number Theory 86 (2001), no. 1, 133--155.  

[13] On the average number of unitary factors of finite abelian groups. II. Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 549--554.  

[12] On three-dimensional divisor problem of $(a,a,b)$ type. Adv. Math. (China) 29 (2000), no. 2, 137--146.  

[11] Number of $\scr B$-free numbers in short intervals. Chinese Sci. Bull. 45 (2000), no. 3, 208--212.

[10] (with  X. D. Cao) On the distribution of $r$-full and $l$-free integers in short intervals. Monatsh. Math. 130 (2000), no. 1, 71--84.

[9] (with  X. D. Cao) Multiple exponential sums with monomials. Acta Arith. 92 (2000), no. 3, 195--213.

[8] On the $k$-dimensional Piatetski-Shapiro prime number theorem. Sci. China Ser. A 42 (1999), no. 11, 1173--1183.  

[7] (with  X. D. Cao) On the distribution of $p\sp \alpha$ modulo one. J. Théor. Nombres Bordeaux 11 (1999), no. 2, 407--423.  

[6] On sums and differences of two coprime $k$th powers. Acta Arith. 91 (1999), no. 3, 233--248.

[5] On the average number of direct factors of finite abelian groups. II. Acta Arith. 90 (1999), no. 1, 69--78.  

[4] (with  X. D. Cao) On the number of coprime integer pairs within a circle. Acta Arith. 90 (1999), no. 1, 1--16.

[3] (with  X. D. Cao) The distribution of square-free numbers of the form $[n\sp c]$. J. Théor. Nombres Bordeaux 10 (1998), no. 2, 287--299.  

[2] (with  X. D. Cao)  On the average number of unitary factors of finite abelian groups. Acta Arith. 85 (1998), no. 4, 293--300.