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. 
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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/

[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.