# On a diophantine inequality involving prime numbers

Acta Arithmetica (1992)

- Volume: 61, Issue: 3, page 289-306
- ISSN: 0065-1036

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topD. I. Tolev. "On a diophantine inequality involving prime numbers." Acta Arithmetica 61.3 (1992): 289-306. <http://eudml.org/doc/206467>.

@article{D1992,

author = {D. I. Tolev},

journal = {Acta Arithmetica},

keywords = {Goldbach-Waring type problem; zero density estimates; zero-free regions; Riemann zeta-function; exponential sums},

language = {eng},

number = {3},

pages = {289-306},

title = {On a diophantine inequality involving prime numbers},

url = {http://eudml.org/doc/206467},

volume = {61},

year = {1992},

}

TY - JOUR

AU - D. I. Tolev

TI - On a diophantine inequality involving prime numbers

JO - Acta Arithmetica

PY - 1992

VL - 61

IS - 3

SP - 289

EP - 306

LA - eng

KW - Goldbach-Waring type problem; zero density estimates; zero-free regions; Riemann zeta-function; exponential sums

UR - http://eudml.org/doc/206467

ER -

## References

top- [1] S. A. Gritsenko, On a problem of I. M. Vinogradov, Mat. Zametki 39 (1987), 625-640 (in Russian).
- [2] M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170. Zbl0241.10026
- [3] A. A. Karatsuba, Principles of Analytic Number Theory, Nauka, Moscow 1983 (in Russian).
- [4] I. I. Piatetski-Shapiro, On a variant of Waring-Goldbach's problem, Mat. Sb. 30 (72) (1) (1952), 105-120 (in Russian). Zbl0047.28001
- [5] B. I. Segal, On a theorem analogous to Waring's theorem, Dokl. Akad. Nauk SSSR (N. S.) 2 (1933), 47-49 (in Russian). Zbl0008.24303
- [6] E. G. Titchmarsh, The Theory of the Riemann Zeta-function (revised by D. R. Heath-Brown), Clarendon Press, Oxford 1986. Zbl0601.10026
- [7] D. I. Tolev, Diophantine inequalities involving prime numbers, Thesis, Moscow University, 1990 (in Russian). Zbl0762.11033
- [8] R. C. Vaughan, On the distribution of αp modulo 1, Mathematika 24 (1977), 135-141.

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