OALib Journal期刊
ISSN: 2333-9721
费用:99美元
|
|
|
关于二项指数和的均值
Keywords: 二项指数和,均值,渐进公式,中国剩余定理
Abstract:
针对著名的Smararadche问题,有很多有趣的均值及相应的渐近公式,利用这些函数的均值及渐进公式可以为工程或其它方面的需要进行估值,指数和的均值计算是其中很重要的问题之一.尤其是近年来,人们引入了二项指数和,给出了一些特殊情况下二项指数和复合后函数的均值.推广了这些结果,给出了二项指数和C(m,n,h,k;q)关于正整数q的一个递归公式,以及q=pα(α≥1)时某些特定条件下C(m,n,h,k;q)的均值,其中p为奇素数.
References
[1] | Smararadche F. Only Problems, Not Solutions[M]. Chicago:Xiquan Publishing House,1993.
|
[2] | 徐哲峰. 一些新的数论函数及其均值公式[J]. 数学学报,2006,49(1):77-80.
|
[3] | 郑家兵,廖群英. 关于正整数n的r次可加补数[J]. 四川师范大学学报:自然科学版,2013,36(3):324-327.
|
[4] | Xu Z F. On the additive k-power complement[C]//Researh on Smararadche Problems in Number Theory. Phoenix:Hexis,2004.
|
[5] | Hua L K. On exponential sums[J]. Sci Record,1957,1:1-4.
|
[6] | Cochrane T, Zheng Z Y. Bounds for certain exponential sums[J]. Asian J Math,2000,4(4):757-774.
|
[7] | Liu H N. Mean value of mixed exponential sums[J]. Proc Am Math Soc,2008,136(4):1193-1203.
|
[8] | Wang T T, Pan X W. The mean value involving Dedekind sums and two-term exponential sums[J]. Science in China,2012,55(3):557-565.
|
[9] | He Y, Liao Q Y. On the mean value of general k-th Gauss sums[J]. J Math Research Appl,2011,3(6):1009-1014.
|
[10] | Apostol M T. Introduction to Analytic Number Theory[M]. New York:Springer-Verlag,1976:157-162.
|
[11] | Cochrane T, Piner C. A further refinement of mordell's bound on exponential sums[J]. Acta Arith,2005,116:35-41.
|
[12] | Cochrane T. Using stepanov's method for exponential sums involving rational functions[J]. J Number Theory,2006,116:270-292.
|
[13] | Zhang T P. On mixed two-term exponential sums[J]. J Korean Math Soc,2010,47(6):1107-1122.
|
[14] | Yang P, Cai T X. On the divisibility of multinomial exponent sums[J]. Adv Math(China),2014,43(3):387-397.
|
[15] | Li J H, Zhang W P. A hybrid mean value involving the Dedekind sums and exponential sums[J]. Adv Math(China),2014,43(4):527-533.
|
Full-Text
|
|
Contact Us
service@oalib.com QQ:3279437679 
WhatsApp +8615387084133
|
|