Geodesic
The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands
Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 410-420

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An asymptotic formula in the generalized Estermann ternary problem for noninteger powers with almost equal summands dealing with the representation of a sufficiently large natural number as the sum of two primes and the integer part of a noninteger power of a natural number is proved.
Keywords: Estermann problem, almost equal summands, short trigonometric sum with noninteger exponent, density theorem. 
@article{MZM_2016_100_3_a7,
     author = {P. Z. Rakhmonov},
     title = {The {Generalized} {Estermann} {Ternary} {Problem} for {Noninteger} {Powers} with {Almost} {Equal} {Summands}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {410--420},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a7/}
}
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P. Z. Rakhmonov. The Generalized Estermann Ternary Problem for Noninteger Powers with Almost Equal Summands. Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 410-420. http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a7/