Geodesic
Estermann's Ternary Problem with Almost Equal Summands
Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 564-572 
Z. Kh. Rakhmonov. Estermann's Ternary Problem with Almost Equal Summands. Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 564-572. http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a9/
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     title = {Estermann's {Ternary} {Problem} with {Almost} {Equal} {Summands}},
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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 positive integer N as the sum of two primes and the square of a natural number when they are almost equal.

[1] Estermann T., “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., “Srednie znacheniya funktsii Chebysheva v korotkikh intervalakh”, Sovremennye problemy matematiki i mekhaniki, Tr. mezhdunarodnoi konferentsii, posvyaschennoi 175-letiyu P. L. Chebysheva, MGU, M., 1996, 125–189

[3] Rakhmonov Z. Kh., “Korotkie lineinye trigonometricheskie summy s prostymi chislami”, Dokl. AN RT, 43:3 (2000)

[4] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Teoriya kratnykh trigonometricheskikh summ, Nauka, M., 1987

[5] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1976

[6] Zhan Tao, “On represention of a large odd integer as a sum of three almost primes”, Acta Math. Sinica, 7:3 (1991), 259–272 | DOI | MR | Zbl