Abstract
We investigate the exceptional sets of natural number n which can be represented as sums of five and six cubes of almost equal primes, i.e. \({n=p_1^3+\cdots+p_s^3}\) (s=5,6). It is established that almost all natural numbers n subject to certain congruence conditions have the above representation with \({|p_j-(n/s)^{\frac{1}{3}}|\leq n^{\theta_s/3+\varepsilon}}\) (\({1\leq j\leq s}\)), where \({\theta_5=8/9+\varepsilon}\) and \({\theta_6=5/6+\varepsilon}\).
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Wang, M. Exceptional sets for sums of five and six almost equal prime cubes. Acta Math. Hungar. 156, 424–434 (2018). https://doi.org/10.1007/s10474-018-0887-7
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DOI: https://doi.org/10.1007/s10474-018-0887-7