×

zbMATH — the first resource for mathematics

One Diophantine inequality with unlike powers of prime variables. (English) Zbl 1428.11068

MSC:
11D75 Diophantine inequalities
11P55 Applications of the Hardy-Littlewood method
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baker, A., On some Diophantine inequalities involving primes, J. Reine Angew. Math., 228, 166-181, (1967) · Zbl 0155.09202
[2] Baker, R. C.; Harman, G., Diophantine approximation by prime numbers, J. London Math. Soc., 25, 2, 201-215, (1982) · Zbl 0443.10015
[3] J. Bourgain, On the Vinogradov mean value, preprint (2016); . · Zbl 1371.11138
[4] Bourgain, J.; Demeter, C.; Guth, L., Proof of the main conjecture in vinogradov’s Mean value theorem for degrees higher than three, Ann. of Math., 184, 2, 633-682, (2016) · Zbl 1408.11083
[5] Davenport, H.; Heilbronn, H., On indefinite quadratic forms in five variables, J. London Math. Soc., 21, 185-193, (1946) · Zbl 0060.11914
[6] Ge, W. X.; Li, W. P., One Diophantine inequality with unlike powers of prime variables, J. Inequal. Appl., 2016, 8, (2016) · Zbl 1382.11032
[7] Harman, G., Trigonometric sums over primes I, Mathematika, 28, 249-254, (1981) · Zbl 0465.10029
[8] Harman, G., Diophantine approximation by prime numbers, J. London Math. Soc., 44, 2, 218-226, (1991) · Zbl 0754.11010
[9] Languasco, A.; Settimi, V., On a Diophantine problem with one prime, two squares of primes and \(s\) powers of two, Acta Arith., 154, 4, 385-412, (2012) · Zbl 1306.11031
[10] Languasco, A.; Zaccagnini, A., A Diophantine problem with a prime and three squares of primes, J. Number Theory, 132, 3016-3028, (2012) · Zbl 1306.11032
[11] Languasco, A.; Zaccagnini, A., On a ternary Diophantine problem with mixed powers of primes, Acta Arith., 159, 4, 345-362, (2013) · Zbl 1330.11063
[12] Li, W. P.; Wang, T. Z., Diophantine approximation with one prime and three squares of primes, Ramanujan J., 25, 343-357, (2011) · Zbl 1234.11036
[13] Li, W. P.; Wang, T. Z., Diophantine approximation with two primes and one square of prime, Chin. Quart. J. Math., 27, 3, 417-423, (2012) · Zbl 1274.11111
[14] Liu, Z. X.; Sun, H. W., Diophantine approximation with one prime and three squares of primes, Ramanujan J., 30, 327-340, (2013) · Zbl 1281.11029
[15] Matomäki, K., Diophantine approximation by primes, Glasgow Math. J., 52, 87-106, (2010) · Zbl 1257.11035
[16] Mu, Q. W.; Qu, Y. Y., A Diophantine inequality with prime variables and mixed power, Acta Math. Sinica (Chin. Ser.), 58, 3, 491-500, (2015) · Zbl 1340.11055
[17] Ramachandra, K., On the sums \(\sum_{j = 1}^K f_j(p_j)(\lambda_j)\) fixed non-zero real numbers, \(f_j(x)\) fixed polynomials and \(p_j\) arbitrary primes), J. Reine Angew. Math., 262/263, 158-165, (1973) · Zbl 0266.10017
[18] Titchmarsh, E. C.; Heath-Brown, D. R., The Theory of the Riemann Zeta-Function, (1986), Oxford University Press, Oxford
[19] Vaughan, R. C., Diophantine approximation by prime numbers, I, Proc. London Math. Soc., 28, 3, 373-384, (1974) · Zbl 0274.10045
[20] Vaughan, R. C., Diophantine approximation by prime numbers, II, Proc. London Math. Soc., 28, 3, 385-401, (1974) · Zbl 0276.10031
[21] Vaughan, R. C., The Hardy-Littlewood Method, (1997), Cambridge University Press, Cambridge · Zbl 0868.11046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.