Geodesic
Generalized Estermann’s ternary problem for noninteger powers with almost equal summands
Čebyševskij sbornik, Tome 16 (2015) no. 1, pp. 248-253

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An asymptotic formula is obtained in generalized Estermann's ternary problem for noninteger powers with almost equal summands on the representations of a sufficiently large natural number as a sum of two primes and integer part of noninteger power of a natural number. Bibliography: 9 titles.
Keywords: exponential sums, Estermann's ternary problem with noninteger exponents, almost equal summands. 
P. Z. Rakhmonov. Generalized Estermann’s ternary problem for noninteger powers with almost equal summands. Čebyševskij sbornik, Tome 16 (2015) no. 1, pp. 248-253. http://geodesic.mathdoc.fr/item/CHEB_2015_16_1_a13/
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[1] T. Estermann, “Proof that every large integer is the sum of two primes and square”, Proc. London Math. Soc., 11 (1937), 501–516 | DOI

[2] Rakhmonov Z. Kh., “Estermann's Ternary Problem with Almost Equal Summands”, Mathematical Notes, 74:4 (2003), 534–542 | DOI | DOI

[3] Rakhmonov Z. Kh., “The Estermann cubic problem with almost equal summands”, Mathematical Notes, 95:4 (2014), 407–417 | DOI | DOI

[4] Rakhmonov P. Z., “Short sums with a noninteger power of a natural number”, Mathematical Notes, 95:5 (2014), 697–707 (Russian) | DOI | DOI

[5] Rakhmonov P. Z., “Short exponential sums with a non-integer power of a natural number”, Moscow University Mathematics Bulletin, 68:1 (2013), 65–68 | DOI

[6] Karatsuba A. A., Fundamentals of Analytic Number Theory, 2nd edition, Nauka, M., 1983, 240 pp. (Russian)

[7] Voronin S. M., Karatsuba A. A., The Riemann Zeta–Function, Fizmatlit, M., 1994, 376 pp. (Russian)

[8] Rakhmonov Z. Kh., “Estimate of the density of the zeros of the Riemann zeta function”, Russian Mathematical Surveys, 49:2 (1994), 168–169 | DOI

[9] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Trigonometric sums in number theory and analysis, Walter de Gruyter, Berlin–New–York, 2004, 554 pp.