On the number of nonzero digits of the partition function |
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| Authors: | Florian Luca |
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| Affiliation: | 1. Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
2. The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, P.O. Wits 2050, Johannesburg, South Africa
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| Abstract: | Let p(n) be the function that counts the number of partitions of n. Let b ≥ 2 be a fixed positive integer. In this paper, we show that for almost all n the sum of the digits of p(n) in base b is at least log n/(7log log n). Our proof uses the first term of Rademacher’s formula for p(n). |
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