On the Number of Optimal Base 2 Representations of Integers |
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| Authors: | Peter J. Grabner Clemens Heuberger |
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| Affiliation: | 1. Institut für Mathematik A, Technische Universit?t Graz, Steyrergasse 30, 8010, Graz, Austria
2. Institut für Mathematik B, Technische Universit?t Graz, Steyrergasse 30, 8010, Graz, Austria
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| Abstract: | We study representations of integers n in binary expansions using the digits 0,±1. We analyze the average number of such representations of minimal “weight” (= number of non-zero digits). The asymptotic main term of this average involves a periodically oscillating function, which is analyzed in some detail. The main tool is the construction of a measure on [−1,1], which encodes the number of representations. AMS Classification (2000) Primary: 11A63 Secondary: 11K16 · 11K55 · 68W40 · 94A60 |
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| Keywords: | Signed digit expansions Minimal Hamming weight Elliptic curve cryptography |
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