A diophantine inequality involving prime powers

• Autorzy: A. Kumchev
• Języki publikacji: EN

Kategorie tematyczne

• 11N36: Applications of sieve methods
• 11P32: Goldbach-type theorems; other additive questions involving primes
• 11P55: Applications of the Hardy-Littlewood method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 89
• Numer: 4
• Strony: 311-330

Daty

wydano

1999

otrzymano

1998-10-23

Twórcy

autor

A. Kumchev

• Department of Mathematics, University of South Carolina, Columbia, SC 29208 U.S.A.

Bibliografia

• [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.
• [3] G. Harman, On the distribution of αp modulo one, J. London Math. Soc. (2) 27 (1983), 9-18.
• [4] G. Harman, On the distribution of αp modulo one II, Proc. London Math. Soc. (3) 72 (1996), 241-260.
• [5] A. Kumchev and T. Nedeva, On an equation with prime numbers, Acta Arith. 83 (1998), 117-126.
• [6] H.-Q. Liu, On square-full numbers in short intervals, Acta Math. Sinica (N.S.) 65 (1993), 148-164.
• [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.
• [8] I. I. Piatetski-Shapiro, On a variant of the Waring-Goldbach problem, Mat. Sb. 30 (1952), 105-120 (in Russian).
• [9] P. Sargos and J. Wu, Multiple exponential sums with monomials and their applications in number theory, preprint, 1997.
• [10] D. I. Tolev, On a diophantine inequality involving prime numbers, Acta Arith. 61 (1992), 289-306.
• [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).