Digital Sum Problems for the p-adic Expansion of Natural Numbers
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概要
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Let p be a positive integer greater than 1 and denote the p-adic expansion of n ∈N by n =∑i ≥0αi (n )p i, where αi (n ) ∈{0,1,…,p −1}. We set s (n,l ) =∑i ≥01{αi (n)=l } for l =1,2,…,p −1, and s (n ) =∑l =1p −1l s (n,l ). We define the power sum of sum of digits by Sk(N ) =∑n =0N −1s (n )k, k ∈N, and the exponential sum of sum of digits by F (ξ ,N ) =∑n =0N −1e ξs(n), ξ ∈R for N ∈N. Explicit formulas of these sums have been investigated by many authors for a long time. In this paper, developing our previous results, we shall give explicit formulas of F (ξ ,N ) and Sk(N ).
- 東北大学の論文
著者
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OKADA Tatsuya
Department of Mechanical Engineering, Faculty of Engineering, The University of Tokushima
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Okada Tatsuya
Department Of Mathematics School Of Medicine Fukushima Medical University
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Sekiguchi Takeshi
Information Science, Liberal Arts, Tohoku Gakuin University
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Shiota Yasunobu
Information Science, Liberal Arts, Tohoku Gakuin University
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Yasunobu Shiota
Information Science Tohoku Gakuin University
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Shiota Yasunobu
Information Science Liberal Arts Tohoku Gakuin University
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MURAMOTO Katsushi
Kawaijuku Educational Institution
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Takeshi Sekiguchi
Information Science Tohoku Gakuin University
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Sekiguchi Takeshi
Information Science Liberal Arts Tohoku Gakuin University
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