Asymptotic formula in the Waring’s problem with almost proportional summands
https://doi.org/10.22405/2226-8383-2024-25-2-139-168
Abstract
For 𝑛 ≥ 3, an asymptotic formula is derived for the number of representations of a sufficiently
large natural number 𝑁 as a sum of 𝑟 = 2𝑛 + 1 summands, each of which is an 𝑛-th power of
natural numbers 𝑥𝑖, 𝑖 = 1, 𝑟, satisfying the conditions
where 𝜇1, . . . , 𝜇𝑟 are positive fixed numbers, and 𝜇1 +. . .+𝜇𝑛 = 1. This result strengthens the theorem of E.M.Wright.
About the Authors
Zarullo Khusenovich Rakhmonov
A. Dzhuraev Institute of Mathematics
Tajikistan
Tajikistan
doctor of physical and mathematical sciences, professor,
academician of the NAS of Tajikistan
Firuz Zarulloevich Rakhmonov
A. Dzhuraev Institute of Mathematics
Tajikistan
Tajikistan
candidate of physical and mathematical sciences
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Review
For citations:
Rakhmonov Z.Kh., Rakhmonov F.Z. Asymptotic formula in the Waring’s problem with almost proportional summands. Chebyshevskii Sbornik. 2024;25(2):139-168. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-2-139-168
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