# A diophantine inequality involving prime powers

Acta Arithmetica (1999)

- Volume: 89, Issue: 4, page 311-330
- ISSN: 0065-1036

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topA. Kumchev. "A diophantine inequality involving prime powers." Acta Arithmetica 89.4 (1999): 311-330. <http://eudml.org/doc/207274>.

@article{A1999,

author = {A. Kumchev},

journal = {Acta Arithmetica},

keywords = {Diophantine inequality; prime numbers},

language = {eng},

number = {4},

pages = {311-330},

title = {A diophantine inequality involving prime powers},

url = {http://eudml.org/doc/207274},

volume = {89},

year = {1999},

}

TY - JOUR

AU - A. Kumchev

TI - A diophantine inequality involving prime powers

JO - Acta Arithmetica

PY - 1999

VL - 89

IS - 4

SP - 311

EP - 330

LA - eng

KW - Diophantine inequality; prime numbers

UR - http://eudml.org/doc/207274

ER -

## References

top- [1] Y. C. Cai, On a diophantine inequality involving prime numbers, Acta Math. Sinica 39 (1996), 733-742 (in Chinese).
- [2] J. B. Friedlander, Integers free from large and small primes, Proc. London Math. Soc. (3) 33 (1976), 565-576. Zbl0344.10021
- [3] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-18. Zbl0504.10018
- [4] G. Harman, On the distribution of αp modulo one II, Proc. London Math. Soc. (3) 72 (1996), 241-260. Zbl0874.11052
- [5] A. Kumchev and T. Nedeva, On an equation with prime numbers, Acta Arith. 83 (1998), 117-126. Zbl1023.11054
- [6] H.-Q. Liu, On square-full numbers in short intervals, Acta Math. Sinica (N.S.) 65 (1993), 148-164. Zbl0708.11044
- [7] H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, CBMS Regional Conf. Ser. in Math., Amer. Math. Soc., Providence, R.I., 1994. Zbl0814.11001
- [8] I. I. Piatetski-Shapiro, On a variant of the Waring-Goldbach problem, Mat. Sb. 30 (1952), 105-120 (in Russian). Zbl0047.28001
- [9] P. Sargos and J. Wu, Multiple exponential sums with monomials and their applications in number theory, preprint, 1997. Zbl0963.11045
- [10] D. I. Tolev, On a diophantine inequality involving prime numbers, Acta Arith. 61 (1992), 289-306. Zbl0762.11033
- [11] I. M. Vinogradov, Representation of an odd number as the sum of three primes, Dokl. Akad. Nauk SSSR 15 (1937), 291-294 (in Russian).

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