Welcome to Zhi-Hong Sun's Home Page

         Zhi-Hong Sun(孙智宏)         

School of Mathematical Sciences

Huaiyin Normal University

Huaian, Jiangsu 223001

The People's Republic of China

Email: zhihongsun@yahoo.com



This page has been visited times since February 25, 2003.

Last modified: April 11, 2014

Born: 16 October 1965 in Lianshui,Jiangsu, PR China

Research Areas: Number theory(数论), Combinatorics(组合数学),Extremal graph theory(极值图论)Special functions(特殊函数

Curriculum vitae  

Awards and Honours (Chinese)

  江苏省普通高等学校优秀青年骨干教师(1994,1996);  全国师范院校曾宪梓教师奖三等奖(1999);  江苏省师德模范(2000); 江苏省中青年学术带头人(2002); 江苏省优秀教育工作者(2004);全国优秀教师(2007);江苏省大学生最喜爱的教师(2011);美国数学评论评论员(Reviewer for Mathematical Reviews, 2001.2-); 美国数学会会员Member of American Mathematical Society, 2004.4-).

Lecture Notes I (English):  1. Congruences for Fibonacci numbers   

                               2. Some conjectures on congruences  

                               3. p-regular functions and congruences for Bernoulli and Euler numbers

                               4. Cubic, quartic, octic residues and Lucas sequences

                               5. Binary quadratic forms and sums of triangular numbers   

                               6. Legendre polynomials and Jacobsthal sums

                               7. Turan's problem and Ramsey numbers for trees         

Lecture Notes II (Chinese): 1. 伟大数学家简介   2.数学研究名言录 3.数学基础和数学哲学 4.同余覆盖系 5.Fibonacci数  6.费尔马大定理 7.华林问题  8. 数论中的互反律 9. 四次多项式模素数的不同取值个数 10. p-正则函数及有关恒等式和同余式 11. 数学和数学家的故事 12. 数论史话

Lecture Notes III(Chinese): 1.卓越的人生艺术 2.怎样做研究工作 3.课堂教学艺术 4.人类航天史话 5.科学简史 6.从亚里斯多德到开普勒的天文学 7.伽利略和牛顿

Links to Number-Theory-Web ,Prime PagesMath News, Biographies of Mathematicians and Rational Cubic  Reciprocity (Paul Pollack's talk).


Preprints in arXiv 

List of  Zhi-Hong Sun's Publications

56.  Z.H.Sun, Congruences concerning Lucas sequences, Int. J. Number Theory 10(2014), no.3, 793-815.

55.  Z.H.Sun, Legendre polynomials and supercongruences, Acta Arith. 159(2013), no.2, 169-200.

54.  Z.H.Sun, Congruences concerning Legendre polynomials III, Int. J. Number Theory 9(2013), no. 4, 965-999.

53.  Z.H.Sun, On the quartic character of quadratic units, Acta Arith. 159(2013), no.1, 89-100.

52.  Z.H.Sun, Congruences for q[p/8] (mod p), Acta Arith. 159(2013), no.1, 1-25.

51.  Z.H.Sun, Congruences concerning Legendre polynomials II, J. Number Theory 133(2013), no. 6, 1950-1976.

50.  Z.H.Sun, Congruences involving  , J. Number Theory 133(2013), no.5, 1572-1595.

49.  Z.H.Sun, Some properties of a sequence analogous to Euler numbers, Bull. Austral. Math. Soc. 87(2013), no.3, 425-440.                                                                                             

48.  Z.H.Sun, Some inversion formulas and formulas for Stirling numbers, Graphs and Combinatorics 29(2013), no.4, 1087-1100. available online on March 17, 2012.

47.  Z.H.Sun and L.L.Wang, An extension of Stern's congruence, Int. J. Number Theory 9(2013), no.2, 413-419.

46.  Z.H.Sun, Ramsey numbers for trees, Bull. Austral. Math. Soc. 86(2012), no.1, 164-176.   

45.  Z.H.Sun, Identities and congruences for a new sequence, Int. J. Number Theory 8(2012), no.1, 207-225.

44.  Z.H.Sun, Congruences for sequences similar to Euler numbers, J. Number Theory 132(2012), no.4, 675-700.                              

43.  Z.H.Sun, Constructing x2 for primes p=ax2+by2 , Adv. in Appl. Math. 48(2012), no.1, 106-120. MR2012k:11041.

42.  Z.H.Sun and L.L.Wang, Turan's problem for trees, J. Combin. Number Theory, 3(2011), no.1, 51-69.

41.  Z.H.Sun, Congruences for, Acta Arith. 149(2011), no.3, 275-296.  MR2012f:11006, Zbl 1238.11005.                                                                                       

40.  Z.H.Sun, Congruences concerning Legendre polynomials, Proc. Amer. Math. Soc. 139(2011), no.6, 1915-1929. MR2012c:11007, Zbl 1225.11006.

39.  Z.H.Sun, On the number of representations of n by ax2+by(y-1)/2, ax2+by(3y-1)/2 and ax(x-1)/2+by(3y-1)/2, Acta Arith. 147(2011), no.1, 81-100.  MR2012c:11090, Zbl 1221.11098.

38.  Z.H.Sun, Binary quadratic forms and sums of triangular numbers, Acta Arith. 146(2011), no.3, 257-297.    MR2012b:11058. Zbl 1222.11051.

37.  Z.H.Sun, Euler numbers modulo 2n, Bull. Aust. Math. Soc. 82(2010), no.2, 221-231. MR2011i:11031. Zbl 1203.11027.

36.  Z.H.Sun, On the number of representations of n by ax(x-1)/2+by(y-1)/2, J. Number Theory 129(2009), no.5, 971-989. available online on February 7, 2009. MR2010j:11061.

35.  Z.H.Sun, Quartic, octic residues and Lucas sequences, J. Number Theory 129(2009), no.3, 499-550. available online on December 11, 2008. MR 2009k:11006. Zbl 1183.11001.

34.  Z.H.Sun, The expansion of , Acta Arith. 134(2008), no.1, 11-29. MR2009j:11064.                              

33.  Z.H.Sun, On the quadratic character of quadratic units, J. Number Theory 128(2008), no.5, 1295-1335. available online on November 7, 2007. MR 2009c:11006. Zbl 1137.11003.

32.  Z.H.Sun, Congruences involving Bernoulli and Euler numbers, J. Number Theory 128(2008), no.2, 280-312. available online on March 27, 2007. MR 2008m:11044. Zbl 1154.11010.

31.  Z.H.Sun, Congruences involving Bernoulli polynomials, Discrete Math. 308(2008), no.1, 71-112. available online on March 24, 2007. MR 2009a: 11048. Zbl. 1138.11006.

30.  Z.H.Sun, Cubic residues and binary quadratic forms, J. Number Theory 124(2007), no.1, 62-104. MR 2008c:11006. Zbl 1124.11006.

29.  Z.H.Sun, A criterion for polynomials to be congruent to the product of linear polynomials (mod p), Fibonacci Quart. 44(2006), no.4, 326-329. MR 2008c:11005.

28.  Z.H.Sun, On the number of incongruent residues of   modulo p, J. Number Theory 119(2006), no.2, 210-241. MR 2007f:11003.

27.  Z.H.Sun, Expansions and identities concerning Lucas sequences, Fibonacci Quart. 44(2006), no.2, 145-153.MR 2007h:11023.

26.  Z.H.Sun, Primality tests for numbers of the form , Fibonacci Quart. 44(2006), no.2, 121-130. MR 2007f:11141.

25.  Z.H.Sun and K.S. Williams, Ramanujan identities and Euler products for a type of Dirichlet series, Acta Arithmetica 122(2006), no. 4, 349-393. MR 2007d:11053.

24.  Z.H.Sun and K.S. Williams, On the number of representations of n by , Acta Arithmetica 122(2006), no. 2, 101-171. MR 2008d:11032, Zbl 1095.11024.

23. Z.H.Sun, On the properties of Newton-Euler pairs, J. Number Theory 114(2005), no.1, 88-123. MR 2006g:11028.

22. Z.H.Sun, Quartic residues and binary quadratic forms, J. Number Theory 113(2005), no.1, 10-52. MR 2006a:11002. Zbl 1101.11003.

21. Z.H.Sun, Cubic and quartic congruences modulo a prime, J. Number Theory 102(2003),no.1, 41-89. MR 2004e:11004, Zbl 1033.11003.

20. Z.H.Sun, Values of Lucas sequences modulo primes, Rocky Mountain J. Math. 33(2003),no.3,1123-1145. MR 2005c:11005. Zbl 1076.11009.

19. Z.H.Sun, Consecutive numbers with the same Legendre symbol, Proc. Amer. Math. Soc.130(2002),no.9, 2503-2507. MR 2003d:11008, Zbl.1003.11001.                

18. Z.H.Sun, Five congruences for primes, Fibonacci Quart.40(2002),no.4,345-351. MR 2003k:11004, Zbl.1009.11004.

17. Z.H.Sun, Bernoulli numbers modulo and (Chinese), J. Huaiyin Teachers College(Nat.Sci.Edit.)1(2002),no.1,13-15.

16. Z.H.Sun, Linear recursive sequences and powers of matrices, Fibonacci Quart.39(2001),no.4, 339-351. MR 2002f:11013, Zbl.1003.11002.

15. Z.H.Sun, Invariant sequences under binomial transformation, Fibonacci Quart.39(2001),no.4, 324-333. MR 2002f:11012, Zbl.0987.05013

14. Z.H.Sun, Supplements to the theory of quartic residues, Acta Arithmetica 97(2001),no.4, 361-377. MR 2002c:11007. Zbl 1049.11007.

13. Z.H.Sun, Congruences concerning Bernoulli numbers and Bernoulli polynomials, Discrete Appl. Math. 105(2000),no.1-3,193-223. MR 2001m:11022,Zbl.0990.11008.

12. Z.H.Sun, The inverse matrices, spectral condition numbers and invertible conditions of cyclic matrices (Chinese), J. Huaiyin Teachers College 21(1999), no.3, 6-13.

11. Z.H.Sun, On the theory of cubic residues and nonresidues, Acta Arithmetica 84(1998),no.4, 291-335. MR 99c:11005, Zbl.0912.11002.

10. Z.H.Sun, Congruences for Bernoulli numbers and Bernoulli polynomials, Discrete Mathematics 163(1997),no.1-3,153-163. MR 98b:05001,Zbl.0872.11012.

9. Z.H.Sun, A supplement to the binomial inversion formula(Chinese), J. Nanjing Univ. Math. Biquarterly 12(1995),no.2,264-271. MR 97d:05009, Zbl.0871.11012.(List of the main results)

8. Z.H.Sun, The combinatorial sum and its applications in number theory III(Chinese), J. Nanjing Univ. Math. Biquarterly 12(1995),no.1,90-102. MR 96g:11017,Zbl.0862.11023. (List of the results)

7. Z.H.Sun, The combinatorial sum  and its applications in number theory II(Chinese), J. Nanjing Univ. Math. Biquarterly 10(1993),no.1,105-118. MR 94j:11021, Zbl.0808.11016. (List of the results)

6. Z.H.Sun, The combinatorial sum  and its applications in number theory I(Chinese), J. Nanjing Univ. Math. Biquarterly 9(1992),no.2,227-240. MR 94a:11026, Zbl.0783.11010. (List of the results)

5. Z.H.Sun, Notes on quartic residue symbol and rational reciprocity laws (Chinese), J. Nanjing Univ. Math. Biquarterly 9(1992),no.1,92-101. MR 94b:11007, Zbl.0791.11001.(List of the results)

4. Z.H.Sun and Z.W.Sun, Fibonacci numbers and Fermat's last theorem, Acta Arithmetica 60(1992),no.4, 371-388. MR 93e:11025, Zbl.0725.11009.

3. Z.H.Sun, Maximum size of graphs with girth not less than a given number (Chinese), J. Nanjing Univ. 27(1991),Special Issue,43-50,146. MR 93b:05086. (List of the main results)

2. Z.H.Sun, A class of problems of Turan type (Chinese), J. Nanjing Univ. Math. Biquarterly 8(1991),no.1,87-98. MR 92m:05106. (List of the results)

1. Z.W.Sun and Z.H.Sun, Some results on covering systems of congruences (Chinese), J. Southwest Teachers Univ. (Nat.Sci.Edit.)(1987), no.1, 10-15. Zbl.0749.11018.