Geodesic
Arithmetical applications for estimates of Weyl's sums of increasing degree polynomials
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 2, pp. 595-640.

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This paper gives applications of estimates of Weyl's sums to computations of constants in the modern bound of the Riemann's zeta-function zeros as well as to deduction of asymptotical formulae in ternary additive problems with primes, where one of the variables grows faster than the polynomial. 
@article{FPM_1998_4_2_a9,
     author = {O. V. Popov},
     title = {Arithmetical applications for estimates of {Weyl's} sums of increasing degree polynomials},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {595--640},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a9/}
}
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O. V. Popov. Arithmetical applications for estimates of Weyl's sums of increasing degree polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 2, pp. 595-640. http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a9/