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Additive functions at consecutive integers

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Abstract

Additive functions f 0,…,f k satisfying the relation

$$\liminf_{x\to\infty}\frac{1}{x}\sum_{n\leqq x} \|f_0(n)+ \dots+f_k(n+k) +\Gamma\| =0 $$

are characterized for those f j for which ∥f j (p)∥≦η holds for every prime p, and η is a suitable small positive number, \(\|z\| =\min_{k\in\mathbb{Z}} {|z-k|}\).

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Authors and Affiliations

  1. Department of Computer Algebra, Eötvös Loránd University, H-1117, Budapest, Pázmány Péter sétány 1/C, Hungary

    Bui Minh Phong

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  1. Bui Minh Phong
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Correspondence to Bui Minh Phong.

Additional information

This work was completed with the support of the Hungarian and Vietnamese TET (grant agreement no. TET 10-1-2011-0645).

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Phong, B.M. Additive functions at consecutive integers. Acta Math Hung 142, 260–274 (2014). https://doi.org/10.1007/s10474-013-0337-5

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  • DOI: https://doi.org/10.1007/s10474-013-0337-5

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