
翟文广 教授，博士生导师
民族： 汉 性别：男
Email: zhaiwg@hotmail.com， wgzhai@163.com
主要学术论文
[68](with Deyu Zhang) On the mean value of the index of composition of an integral ideal, Journal of Number Theory 131 (2011), 618–633.
[67](with Deyu Zhang) On the fifthpower moment of (x), Int. J of Number Theory, Vol. 7(2011), 7186.
[66](with Xiaodong Cao, Yoshio Tanigawa), On a conjecture of Chowla and Walum, Sci. China Math. 53 (2010), no. 10, 2755–2771.
[65](with Jun Furuya, Yoshio Tanigawa), Dirichlet series obtained from the error term in the Dirichlet divisor problem, Monatsh. Math. 160 (2010), no. 4, 385–402
[64](with Xiaodong Cao), On the mean square of the error term for the asymmetric twodimensional divisor problems, Monatsh. Math. 160 (2010), no. 2, 115–142.
[63](with Deyu Zhang), Mean values of a gcdsum function over regular integers modulo n, J. Integer Seq. 13 (2010), no. 4, Article 10.4.7, 11 pp.
[62](with Xiaodong Cao)Some arithmetic functions involving exponential divisors, J. Integer Seq. 13 (2010), no. 3, Article 10.3.7, 13 pp.
[61](with Xiaodong Cao)On the mean square of the error term for the asymmetric twodimensional divisor problem, Monatsh. Math. 159 (2010), no. 12, 185–209.
[60](with Lingling Dong ) ON the distribution of {x/p}(in Chinese)， Acta Math. Sinica，52 (2009), no. 3, 569–578.
[59]On the prime power factorization of n!, J. Number Theory 129 (2009), no. 8, 1820–1836.
[58]On the error term inWeyl’s law for the Heisenberg manifolds. II, Sci. China Ser. A 52 (2009), no. 5, 857–874.
[57](with Yoshio Tanigawa), On the fourth power moment of (x) and E(x) in short intervals,
Int. J. Number Theory 5 (2009), no. 2, 355–382.
[56](with Huaning Liu),A note on the pseudorandomness of the Liouville function, Acta Arith. 136 (2009), no. 2, 101–121.
[55](with Gaangshi Lv)On the representation of large integers as sums of four almost equal squares of primes, Ramanujan J. 18 (2009), no. 1, 1–10.
[54] (with Xiaodong Cao) Distribution of squarefree integers of the form (in Chinese)，Acta Math. Sinica51(2008), no. 6, 1187–1194.
[53]On the error term in Weyl’s law for Heisenberg manifolds, Acta Arith. 134 (2008), no. 3, 219–257.
[52](with Jun Furuya)On the kfree divisor problem(II), Acta Arith. 132 (2008), 351358
[51](with Yoshio Tanigawa) On the gcdsum function, J. Integer Seq. 11 (2008), no. 2, Article 08.2.3, 11 pp.
[50](with Yoshio Tanigawa, Deyu Zhang)On the RankinSelberg problem: higher power moments of the Riesz mean error term, Sci. China Ser. A 51 (2008), no. 1, 148160. ?
[49] (with Xiaodong Cao) On a Diophantine inequality over primes. II, Monatsh. Math. 150 (2007), no. 2, 173179 ?
[48](with Yoshio Tanigawa) Dirichlet series associated with polynomials and applications, J. Number Theory 122 (2007), no. 2, 466518 ?
[47] Rényi's problem in short intervals, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 1, 29—36
[46]On the mean value of the index of composition of an integer, Acta Arith. 125 (2006), no. 4, 331345 ?
[45](with Deyu Zhang)Differences of two relatively prime cubes. (Chinese) Acta Math. Sinica (Chin. Ser.) 49 (2006), no. 5, 11811188.
[44]On the kfree divisor problem, Acta Arith. 123 (2006), no. 3, 267287(SCI)
[43](with Deyu Zhang)On integers $n$ coprime to $[n\sp c]$. (Chinese) Acta Math. Sinica (Chin. Ser.) 49 (2006), no. 2, 469472
[42]On higherpower moments of (x). IV. (Chinese) Acta Math. Sinica (Chin. Ser.) 49 (2006), no. 3, 639646.
[41](with Xiaodong Cao) On sums of two coprime kth powers. II, Monatsh. Math. 148 (2006), no. 2, 153—172
[40](with Deyu Zhang) Estimates of maximal divisor of $k$th power. (Chinese) Acta Math. Sinica (Chin. Ser.) 49 (2006), no. 1, 205214.
[39]Squarefree integers as sums of two squares, Number theory, 219227, Dev. Math., 15, Springer, New York, 2006
[38]On higherpower moments of (x). III, Acta Arith. 118 (2005), no. 3, 263—281
[37] On sums of two coprime kth powers, Monatsh. Math. 144 (2005), no. 3, 233250 ?
[36](with Deyu Zhang) The WaringGoldbach problem in thin sets of primes. II. (Chinese) Acta Math. Sinica (Chin. Ser.) 48 (2005), no. 4, 809816. ?
[35] On higherpower moments of E(t), Acta Arith. 115 (2004), no. 4, 329—348
[34]On higherpower moments of (x). II, Acta Arith. 114 (2004), no. 1, 3554 ?
[33]On higherpower moments of (x), Acta Arith. 112 (2004), no. 4, 367395 ?
[32]The divisor problem for the Beatty sequences. (Chinese) Acta Math. Sinica (Chin. Ser.) 47 (2004), no. 6, 12131216.
[31](with Guangshi Lv) On threedimensional divisor problem of $(a,a,b)$ type. Adv. Math. (China) 33 (2004), no. 2, 195202.
[30]Short interval results for a class of integers, Monatsh. Math. 140 (2003), no. 3, 233257 ?
[29](with Xiaodong Cao) On a binary Diophantine inequality. Adv. Math. (China) 32 (2003), no. 6, 706721.
[28](with Guangshi Lv) The sum of multidimensional divisor functions on a special sequence. (Chinese) Adv. Math. (China) 32 (2003), no. 6, 660664.
[27](with Xiaodong Cao)On a Diophantine inequality over primes. Adv. Math. (China) 32 (2003), no. 1, 6373. ?
[26]On primitive lattice points in planar domains, Acta Arith. 109 (2003), no. 1, 1—26
[25](with Guangshi Lv)A special divisor problem. (Chinese) Acta Math. Sinica (Chin. Ser.) 45 (2002), no. 5, 9911004.
[24]On the number of primitive Pythagorean triangles, Acta Arith. 105 (2002), no. 4, 387403 ?
[23](with Xiaodong Cao)A Diophantine inequality with prime numbers. (Chinese) Acta Math. Sinica (Chin. Ser.) 45 (2002), no. 2, 361—370
[22](with Xiaodong Cao)A Diophantine equation with prime numbers. (Chinese) Acta Math. Sinica (Chin. Ser.) 45 (2002), no. 3, 443454.
[21]On the simultaneous distribution of the fractional parts of different powers of prime numbers, J. Number Theory 86 (2001), no. 1, 133155 ?
[20]On the average number of unitary factors of finite abelian groups. II, Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 549554
[19](with Xiaodong Cao)On the distribution of rfull and lfree integers in short intervals, Monatsh. Math. 130 (2000), no. 1, 71—84
[18](with Xiaodong Cao)]Multiple exponential sums with monomials, Acta Arith. 92 (2000), no. 3, 195—213
[17]On a system of two Diophantine inequalities with prime numbers, Acta Arith. 92 (2000), no. 1, 3146 ?
[16]On threedimensional divisor problem of $(a,a,b)$ type. Adv. Math. (China) 29 (2000), no. 2, 137146
[15]On the kdimensional PiatetskiShapiro prime number theorem, Sci. China Ser. A 42 (1999), no. 11, 11731183 ?
[14](with Xiaodong Cao) On the distribution of ?modulo one, J. Théor. Nombres Bordeaux 11 (1999), no. 2, 407423
[13]On sums and differences of two coprime kth powers, Acta Arith. 91 (1999), no. 3, 233248 ?
[12]The additive completion of kth powers, J. Number Theory 79 (1999), no. 2, 292—300
[11]On the average number of direct factors of finite abelian groups. II, Acta Arith. 90 (1999), no. 1, 6978 ?
[10](with Xiaodong Cao)On the number of coprime integer pairs within a circle, Acta Arith. 90 (1999), no. 1, 116 ?
[9]The reciprocal sums of a class of additive functions. (Chinese) Acta Math. Sinica (Chin. Ser.) 42 (1999), no. 3, 529536
[8](with Xiaodong Cao)The distribution of squarefree numbers of the form [],J. Théor. Nombres Bordeaux 10 (1998), no. 2, 287299
[7]On the average number of unitary factors of finite abelian groups, Acta Arith. 85 (1998), no. 4, 293300 ?
[6]The WaringGoldbach problem in thin sets of primes. (Chinese) Acta Math. Sinica (Chin. Ser.) 41 (1998), no. 3, 595608
[5] A note on a result of Abercrombie, Chinese Sci. Bull. 42 (1997), no. 14, 11511154 ?
[4](with Xiaodong Cao)On the average number of direct factors of finite abelian groups, Acta Arith. 82 (1997), no. 1, 4555 ?
[3]Reciprocal sums of a class of additive functions in short intervals, Chinese Sci. Bull. 42 (1997), no. 2, 102—105
[2] On a multiplicative hybrid problem, Acta Arith. 71 (1995), no. 1, 4753
[1]On the distribution of {x/n}. II, Chinese Sci. Bull. 41 (1996), no. 1, 1—5

