Geodesic
The Estermann Cubic Problem with Almost Equal Summands
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 445-456

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove an asymptotic formula for the number of representations of a sufficiently large natural number $N$ as the sum of two primes $p_1$ and $p_2$ and the cube of a natural number $m$ satisfying the conditions $|p_i-N/3|\le H$, $|m^3-N/3|\le H$, $H\ge N^{5/6}\mathscr L^{10}$.
Keywords: Estermann cubic problem, Weyl sum, Hua estimate, rational trigonometric sum
Mots-clés : prime, Poisson summation formula. 
@article{MZM_2014_95_3_a10,
     author = {Z. Kh. Rakhmonov},
     title = {The {Estermann} {Cubic} {Problem} with {Almost} {Equal} {Summands}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {445--456},
     publisher = {mathdoc},
     volume = {95},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a10/}
}
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Z. Kh. Rakhmonov. The Estermann Cubic Problem with Almost Equal Summands. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 445-456. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a10/