2.主要成果
科研方面主要研究具有密码学意义的伪随机数列与子集。以下是部分论著目录。
A. 著作目录
1. 刘华宁. 数论中的伪随机二进制数列. 北京: 科学出版社, 2008年5月.
B. SCI论文目录
1．张文鹏, 刘华宁. A note on the Cochrane sum and its hybrid mean value formula. Journal of Mathematical Analysis and Applications, 2003, 288(2): 646-659. (SCI，IDS Number: 752PG)
2. 张文鹏, 刘华宁. On the general Gauss sums and their fourth power mean. Osaka Journal of Mathematics, 2005, 42(1): 189-199. (SCI，IDS Number: 920EI)
3. 刘华宁, 张文鹏. On the hybrid mean value of Gauss sums and generalized Bernoulli numbers. Proceedings of the Japan Academy Series A- Mathematical Sciences, 2004, 80(6): 113-115. (SCI，IDS Number: 845WL)
4. 刘华宁, 张文鹏. On certain Hardy sums and their $2m$-th power mean. Osaka Journal of Mathematics, 2004, 41(4): 745-758. (SCI，IDS Number: 895ET)
5. 刘华宁, 张文鹏. On the even power mean of a sum analogous to Dedekind sums. Acta Mathematica Hungarica, 2005, 106(1-2): 67-81. (SCI，IDS Number: 909GW)
6. 刘华宁, 张文鹏. On the squarefree and squarefull numbers. Journal of Mathematics of Kyoto University, 2005, 45(2): 247-255. (SCI，IDS Number: 979KL)
7. 刘华宁, 张文鹏. On a problem of D. H. Lehmer. Acta Mathematica Sinica English Series, 2006, 22(1): 61--68. (SCI，IDS Number: 994EY)
8. 刘华宁, 张文鹏. On the mean value of $L(m,\chi )L(n,\overline \chi )$ at positive integers $m,n\ge 1$. Acta Arithmetica, 2006, 122(1): 51-56. (SCI，IDS Number: 087NE)
9. 刘华宁, 张小蹦. On the mean value of $\frac{L^{'}}{L} (1,\chi)$. Journal of Mathematical Analysis and Applications, 2006, 320(2): 562-577. (SCI，IDS Number: 049FW)
10. 刘华宁, 张文鹏. Hybrid mean value on the difference between a quadratic residue and its inverse modulo $p$. Publicationes Mathematicae Debrecen, 2006, 69(1-2): 227-243. (SCI，IDS Number: 056VO)
11. 刘华宁. New pseudorandom sequences constructed using multiplicative inverses. Acta Arithmetica, 2006, 125(1): 11-19. (SCI，IDS Number: 163FD)
12. 刘华宁, 张文鹏. General Kloosterman sums and the difference between an integer and its inverse modulo $q$. Acta Mathematica Sinica English Series, 2007, 23(1): 77-82. (SCI，IDS Number: 107FZ)
13. 刘华宁, 张文鹏. Hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums. Journal of the Korean Mathematical Society, 2007,44(1): 11-24. (SCI，IDS Number: 123QL)
14. 刘华宁, 张文鹏. Generalized Cochrane sums and Cochrane-Hardy sums, Journal of Number Theory, 2007, 122(2): 415-428. (SCI，IDS Number: 138HG)
15. 刘华宁. A note on local randomness in polynomial random number and random function generators. Applied Mathematics and Computation, 2007, 186(2): 1360-1366. (SCI，IDS Number: 163MK; EI, Accession Number: 071410523951)
16. 刘华宁, 张文鹏. Mean value on the difference between a quadratic residue and its inverse modulo $p$. Acta Mathematica Sinica English Series, 2007, 23(5): 915-924. (SCI，IDS Number: 157VX)
17. 刘华宁. New pseudorandom sequences constructed by quadratic residues and Lehmer numbers. Proceedings of the American Mathematical Society, 2007, 135(5): 1309-1318. (SCI，IDS Number: 139PV)
18. 刘华宁. Some generalizations of Knopp's identity. Bulletin of the Brazilian Mathematical Society, 2007, 38(2): 179-188. (SCI，IDS Number: 187NY)
19. 刘华宁. A note on the upper bound estimate of high-dimensional Cochrane sum. Journal of Number Theory, 2007, 125(1): 7-13. (SCI，IDS Number: 181AG)
20. 刘华宁, 张文鹏. Hybrid mean value results for a generalization on a problem of D.H. Lehmer and Hyper-Kloosterman sums. Osaka Journal of Mathematics, 2007, 44(3): 615-637. (SCI，IDS Number: 230UK)
21. 刘华宁. On the mean values of the homogeneous Dedekind sums and Cochrane sums in short intervals. Journal of the Korean Mathematical Society, 2007, 44(6): 1243-1254. (SCI，IDS Number: 228LG)
22. 刘华宁, 张文鹏. Hybrid mean value for a generalization of a problem of D. H. Lehmer. Acta Arithmetica, 2007, 130(1): 1-17. (SCI，IDS Number: 277OW)
23. 刘华宁. A family of pseudorandom binary sequences constructed by the multiplicative inverse. Acta Arithmetica, 2007, 130(2): 167-180. (SCI，IDS Number: 277OY)
24. 刘华宁. Mean value of mixed exponential sums. Proceedings of the American Mathematical Society, 2008, 136(4): 1193-1203. (SCI，IDS Number: 250OT)
25. 刘华宁, 张文鹏. Hybrid mean value on the difference between an integer and its inverse modulo $q$. Arkiv for Matematik, 2008, 46(2): 337-347. (SCI，IDS Number: 339CF)
26. 刘华宁, 杨存典. On a problem of D. H. Lehmer and pseudorandom binary sequences. Bulletin of the Brazilian Mathematical Society, 2008, 39(3): 387-399. (SCI，IDS Number: 352HL)
27. 刘华宁. On the mean values of Dedekind sums and Hardy sums. Journal of the Korean Mathematical Society, 2009, 46(1): 187-213. (SCI，IDS Number: 391UY)
28. 刘华宁, 翟文广. A note on the pseudorandomness of the Liouville function. Acta Arithmetica, 2009, 136(2): 101-121. (SCI，IDS Number: 514HR)
29. 刘华宁, 张文鹏. Some applications of certain character sums. Rocky Mountain Journal of Mathematics, 2009, 39(2): 573-589. (SCI，IDS Number: 496GI)
30. 刘华宁. A large family of pseudorandom binary lattices. Proceedings of the American Mathematical Society, 2009, 137(3): 793-803. (SCI，IDS Number: 375ZV)
31. 刘华宁, 展涛, 王小云. On the correlation of pseudorandom binary sequences with composite moduli. Publicationes Mathematicae Debrecen, 2009, 74(1-2): 195-214. (SCI, IDS Number: 404MO)
32. 刘华宁, 展涛, 王小云. Large families of elliptic curve pseudorandom binary sequences. Acta Arithmetica, 2009,140(2): 135-144. (SCI, IDS Number: 554EG)
33. 刘华宁. A note on Lehmer $k$-tuples. International Journal of Number Theory, 2009, 5(7): 1169-1178. (SCI, IDS Number: 523SI)
34．刘华宁. Mean value of some exponential sums and applications to Kloosterman sums. Journal of Mathematical Analysis and Applications, 2010,361(1):205-223. (SCI, IDS Number: 536SK)
35. 张小蹦, 刘华宁. Inversion of $L$-functions, general Kloosterman sums weighted by incomplete character sums. Journal of the Korean Mathematical Society，2010, 47(5): 947-965. (SCI, IDS Number: 646HQ)
36. 刘华宁. Gowers uniformity norm and pseudorandom measures of the pseudorandom binary sequences. International Journal of Number Theory, 2011, 7(5): 1279-1302. (SCI, IDS Number: 816PE)
37. 刘华宁, 王小云. On the correlation of pseudorandom binary sequences using additive characters. Publicationes Mathematicae Debrecen, 2011, 79(1-2): 145-170. (SCI, IDS Number: 816CQ)
38. 刘华宁, 翟文广. The equation $n_1n_2=n_3n_4$, the gcd-sum function and the mean values of certain character sums. Acta Arithmetica, 2012, 152(2): 137-157. (SCI, IDS Number: 927BM)
39. 高静, 刘华宁. Dirichlet characters, Gauss sums and inverse $Z$ transform. Abstract and Applied Analysis, vol. 2012, Article ID 821949, 9 pages, 2012. (SCI, IDS Number: 922UH)
40. 刘华宁, 高静. Large families of pseudorandom binary sequences constructed by using the Legendre symbol. Acta Arithmetica, 2012, 154(1): 103-108. (SCI, IDS Number: 998XM)
41. 刘华宁, 高静. On the Gauss sums and generalized Bernoulli numbers. Ukrainian Mathematical Journal, 2012, 64(6): 971-978. (SCI, IDS Number: 050OV)
42. 刘华宁, 高静. Generalized Knopp identities for homogeneous Hardy sums and Cochrane-hardy sums. Czechoslovak Mathematical Journal, 2012, 62(4): 1147-1159. (SCI, IDS Number: 068KA)
43. 高静, 刘华宁. On the mean value of character sums in short intervals. Journal of Computational Analysis and Applications, 2013, 15(1): 65-72. (SCI, IDS Number: 100KL)
44. 杜永光, 刘华宁. On the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum. Czechoslovak Mathematical Journal, 2013, 63(2): 461-473. (SCI, IDS Number: 182RQ)
45．刘华宁, 张婷. On the distribution of square-full numbers in arithmetic progressions. Archiv der Mathematik, 2013, 101(1): 53-64. (SCI, IDS Number: 185JL)
46. 刘华宁. Large families of pseudorandom binary sequences and lattices by using the multiplicative inverse. Acta Arithmetica, 2013, 159(2): 123-131. (SCI, IDS Number: 213SY)
47. 刘华宁, 高静. A note on certain modular constructions of pseudorandom binary sequences with composite moduli. Periodica Mathematica Hungarica, 2013, 67(2): 175-185. (SCI, IDS Number: 238LN)
48. 徐哲峰, 刘华宁. On the mean values of certain character sums. Abstract and Applied Analysis, vol. 2013, Article ID 326597, 19 pages, 2013. (SCI, IDS Number: 266MW)
49. 刘华宁. A family of elliptic curve pseudorandom binary sequences. Designs, Codes and Cryptography, 2014, 73(1): 251-265. (SCI, IDS Number: AK8CZ)
50. 高静, 刘华宁. Dirichlet characters, Gauss sums and arithmetic Fourier transforms. Applied Mathematics-A Journal of Chinese Universities, 2014, 29(3): 307-316. (SCI, IDS Number: AP6RS)
51. 刘华宁, 高静. A note on large families of pseudorandom binary sequences and lattices. Journal of Information Science and Engineering, 2014, 30(5): 1635-1654. (SCI, IDS Number: AP8KV)
52. 刘华宁. Large family of pseudorandom subsets of the set of the integers not exceeding $N$. International Journal of Number Theory, 2014, 10(5): 1121-1141. (SCI, IDS Number: AO0PM)
53. 刘华宁, 宋尔萍. A note on pseudorandom subsets formed by generalized cyclotomic classes. Publicationes Mathematicae Debrecen, 2014, 85(3-4): 257-271. (SCI, IDS Number: AZ0CE)
54. 刘华宁. On the mean values of Dirichlet $L$-functions. Journal of Number Theory, 2015, 147: 172-183. (SCI, IDS Number: AT8PF)
55. 刘华宁, 董慧. On the distribution of consecutive square-free primitive roots modulo $p$. Czechoslovak Mathematical Journal, 2015，65(2): 555-564. (SCI, IDS Number: CL2YV)
56. 张华, 刘华宁. Pseudorandom subsets with composite moduli. Bulletin of the Belgian Mathematical Society – Simon Stevin, 2015, 22(3): 353-375. (SCI, IDS Number: CU0QH)
57. 刘华宁, 张敏. A large family of Boolean functions. Acta Arithmetica, 2016, 172(3): 251-262. (SCI, IDS Number: DC7BK)
58. 刘华宁, 祁玉婵. On multi-dimensional pseudorandom subsets. Journal of Number Theory, 2017, 181: 73-88. (SCI, IDS Number: FG3FG)
59. 刘华宁, 高波. A large family of pseudorandom sequences of $k$ symbols with length $pq$. Acta Arithmetica, 2017, 181.1: 1-26 (SCI, IDS Number: FN6NJ)
60. 曹艳梅, 刘华宁. Large families of subsets arising from Woods problem and their pseudorandomness. Acta Mathematica Hungarica, 2018, 156(1): 204-219. (SCI, IDS Number: GU3LH)
