[1]胡宏.涉及Fibonacci序列的Dedekind和[J].东南大学学报(自然科学版),2004,34(6):869-871.[doi:10.3969/j.issn.1001-0505.2004.06.034]
 Hu Hong.On Dedekind sums involving Fibonacci numbers[J].Journal of Southeast University (Natural Science Edition),2004,34(6):869-871.[doi:10.3969/j.issn.1001-0505.2004.06.034]
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涉及Fibonacci序列的Dedekind和()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
34
期数:
2004年第6期
页码:
869-871
栏目:
数学、物理学、力学
出版日期:
2004-11-20

文章信息/Info

Title:
On Dedekind sums involving Fibonacci numbers
作者:
胡宏
淮阴师范学院数学系, 淮安 223001
Author(s):
Hu Hong
Department of Mathematics, Huaiyin Teachers College, Huaian 223001, China
关键词:
Fibonacci序列 Lucas 序列 Dedekind和
Keywords:
Fibonacci numbers Lucas numbers Dedekind sums
分类号:
O156.1
DOI:
10.3969/j.issn.1001-0505.2004.06.034
摘要:
{Fn}为Fibonacci数,n为自然数.根据Dedekind和的定义及其相关性质,研究了涉及Fibonacci序列的Dedekind和,估计了和式∑mn=1S((Fkn)/(Fk),(Fk(n+1))/(Fk)),其中m为正整数,k为非负奇数,本文的主要结论推广了张文鹏(Fibonacci Quart, 2000, 40(2): 223-226)的一个结果.
Abstract:
Let {Fn} be the Fibonacci numbers, and let n be natural numbers. According to the definition and characteristics of Dedekind sums, Dedekind sums involving Fibonacci numbers is studied. The sum ∑mn=1S((Fkn)/(Fk),(Fk(n+1))/(Fk))is estimated, here m is a positive interger, and k is a nonnegative odd number. The conclusion extends a result from W.P.Zhang(Fibonacci Quart, 2000, 40(2):223-226).

参考文献/References:

[1] Apostol Tom M. Introduction to analytic number theory[M].New York:Spring-Verlag,1976.
[2] Apostol Tom M. Modular functions and Dirichlet series in number theory[M].New York:Spring-Verlag,1976.
[3] Carlitz L.The reciprocity theorem for Dedekind sums [J].Pacific Math, 1953,3:523-527.
[4] Mordell L J.The reciprocity formula for Dedekind sums [J].Amer J Math, 1951,73:593-598.
[5] Myerson G.Dedekind sums and uniform distribution [J]. Number Theory, 1991,28:1803-1807.
[6] Rademacher H.On the transformation of logn(τ)[J]. Indian Math Soc, 1955,19:25-30.
[7] Zhang W P,Yi Y.On the Fibonacci numbers and the Dedekind sums [J].Fibonacci Quart, 2000,40(2):223-226.
[8] Rabinowitzs Stanley.Algorithmic manipulation of 2-order linear recurrences[J]. Fibonacci Quart, 1999,39(2):162-177.
[9] Hu Hong,Sun Zhiwei,Liu Jianxin.Reciprocal sums of 2-order recurrent sequences [J].Fibonacci Quart, 2001,41(3):214-220.

备注/Memo

备注/Memo:
基金项目: 江苏省教育厅自然科学基金资助项目(01KJD110005).
作者简介: 胡宏(1967—),女,副教授,hysyhh@163.com.
更新日期/Last Update: 2004-11-20