Preview

Chebyshevskii Sbornik

Advanced search

GENERALIZED ESTERMANN’S TERNARY PROBLEM FOR NONINTEGER POWERS WITH ALMOST EQUAL SUMMANDS

https://doi.org/10.22405/2226-8383-2015-16-1-248-253

Abstract

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.

About the Author

P. Z. Rakhmonov

Russian Federation


References

1. Estermann, T. 1937, "Proof that every large integer is the sum of two primes and square" , Proc. London Math. Soc., no. 11, pp. 501 – 516. doi: 10.1112/plms/s2-42.1.501

2. Rakhmonov, Z. Kh. 2003, "Estermann’s Ternary Problem with Almost Equal Summands" , Mathematical Notes, vol. 74, Issue 3–4, pp. 534 — 542. (Russian) doi: 10.1023/A:1026199928464

3. Rakhmonov, Z. Kh. 2014, "The Estermann cubic problem with almost equal summands" , Mathematical Notes, vol. 95, Issue 3–4, pp. 407 – 417. (Russian) doi: 10.1134/S0001434614030122

4. Rakhmonov, P. Z. 2014, "Short sums with a noninteger power of a natural number" , Mathematical Notes, vol. 95, Issue 5–6, pp. 697 – 707. (Russian) doi: 10.1134/S0001434614050125

5. Rakhmonov, P. Z. 2013, "Short exponential sums with a non-integer power of a natural number" , Moscow University Mathematics Bulletin, vol. 68, Issue 1, pp. 65 – 68. (Russian) doi: 10.3103/S0027132213010130

6. Karatsuba, A. A. 1983, "Fundamentals of Analytic Number Theory." , Nauka, Moscow, 2nd edition. 240 p. (Russian)

7. Voronin, S. M. & Karatsuba, A. A. 1994, "The Riemann Zeta–Function." , Moscow, Fizmatlit, 370 p. (Russian)

8. Rakhmonov, Z. Kh. 1994, "Estimate of the density of the zeros of the Riemann zeta function" , Russian Mathematical Surveys, vol. 49, Issue 2, pp. 168 – 169. (Russian) doi: 10.1070/RM1994v049n02ABEH002225

9. Arkhipov, G. I., Karatsuba, A. A. & Chubarikov, V. N. 2004, "Trigonometric sums in number theory and analysis." , Berlin–New-York: Walter de Gruyter, 554 p.


Review

For citations:


Rakhmonov P.Z. GENERALIZED ESTERMANN’S TERNARY PROBLEM FOR NONINTEGER POWERS WITH ALMOST EQUAL SUMMANDS. Chebyshevskii Sbornik. 2015;16(1):248-253. (In Russ.) https://doi.org/10.22405/2226-8383-2015-16-1-248-253

Views: 460


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2226-8383 (Print)