| 摘要: |
| 本文研究了涉及双周期Fibonacci{fn}数列和双周期Lucas{ln}数列的Dedekind和的估计问题.利用Dedekind和S (h,k)的解析性质以及双周期Fibonacci数列和双周期Lucas数列的递推关系,获得了∑n=1m(S(f2n,f2n+1)+S(f2n+1,f2n+2))与∑n=1m(S (f2n,f2n+1)+S(l2n+1,l2n+2))的估计式.本文将涉及Dedekind和的线性递推数列的研究推广到了非线性. |
| 关键词: 双周期Fibonacci数列 双周期Lucas数列 Dedekind和 |
| DOI： |
| 分类号:O156.1 |
| 基金项目:国家自然科学基金项目资助(12126357). |
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| THE DEDEKIND SUMS INVOLVING BI-PERIODIC FIBONACCI AND LUCAS SEQUENCES |
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DU Ting-ting, LIU Xiao-ge
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Research Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, China
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| Abstract: |
| This paper investigates the estimation problem of Dedekind sums involving the bi-periodic Fibonacci {fn} and Lucas {ln} sequence. By utilizing the analytic properties of the Dedekind sum S(h， k), and the recurrence relations of bi-periodic Fibonacci {fn} and Lucas {ln} sequence, we derive asymptotic estimates for the sums Σn=1m (S (f2n, f2n+1) + S (f2n+1, f2n+2)) and Σn=1m (S (l2n, l2n+1) + S (l2n+1, l2n+2)). This work extends the study of Dedekind sums from linear recurrence sequences to the nonlinear recurrence sequences. |
| Key words: Bi-periodic Fibonacci sequence Bi-periodic Lucas sequence Dedekind sums |
