Asymptotic formula in generalization of ternary Esterman problem with almost proportional summands
Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 120-137
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For $n \geq 3$, an asymptotic formula for the number of representations of a sufficiently large natural number $N$ in the form $p_1+p_2+m^n=N$, is obtained. Here $p_1$, $p_2$ are prime numbers, and $m$ is a natural number, satisfying the following conditions $$ \left|p_k-\mu_kN\right|\le H, k=1,2, \left|m^n-\mu_3N\right|\le H, H\ge N^{1-\frac1{n(n-1)}}\mathscr{L}^{\frac{2^{n+1}}{n-1}+n-1}. $$
Keywords:
Estermann problem, almost proportional summands, short exponential sum of G. Weyl, small neighborhood of centers of major arcs.
F. Z. Rahmonov. Asymptotic formula in generalization of ternary Esterman problem with almost proportional summands. Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 120-137. http://geodesic.mathdoc.fr/item/CHEB_2024_25_4_a6/
@article{CHEB_2024_25_4_a6,
author = {F. Z. Rahmonov},
title = {Asymptotic formula in generalization of ternary {Esterman} problem with almost proportional summands},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {120--137},
year = {2024},
volume = {25},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_4_a6/}
}