Small prime solutions of a pair of linear equations in five prime variables

Zhen Cui1, Hong Ze Li1
1Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China

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Tài liệu tham khảo

Hua, L. K.: Die Abschätzung von Expontial summen und ihre Angewendung in der Zahlentheorie. Enzykl. Maht. Wiss. Band I, Teil 2, Heft 13, Leipzig (Chinese ed.), Beijing, 1963

Hua, L. K.: Additive Theory of Prime Numbers, Translations of Mathematical Monographs, Vol. 13, Amer. Math. Soc., Providence, R. I. 1965

Liu, M. C., Tsang, K. M.: Small prime solutions of a pair of linear equations in five variables. In: International Symposium in Memory of Hua Loo Keng, Vol. I (Beijing, 1988), 163–182, Springer, Berlin, 1991

Li, H. Z.: A numerical bound for small prime solutions of a pair of linear equations in five variables (in Chinese). Chinese Ann. Math., Ser. A, 24, 777–786 (2003)

Liu, J. Y., Zhan, T.: Sums of five almost equal prime squares (II). Sci. China Ser. A, 41, 710–722 (1998)

Bauer, C., Liu, M. C., Zhan, T.: On a sum of three prime squares. J. Number Theory, 85, 336–359 (2000)

Liu, J. Y., Liu, M. C.: The exceptional set in the four prime squares problem. Illinois Journal of Mathematics, 44, 272–293 (2000)

Ren, X. M.: The Waring-Goldbach problem for cubes. Acta Arith., 287–301 (2000)

Liu, J. Y., Zhan, T.: The exceptional set in Huas theorem for three squares of primes. Acta Mathematica Sinica, English Series, 21, 335–350 (2005)

Stephen Choi, K. K., Kumchev, A.: Mean values of Dirichlet polynomials and applications to linear equations with prime variables. Acta Arith., 123, 125–142 (2006)

Liu, M. C., Wang, T. Z.: A numerical bound for small prime solutions of some ternary linear equations. Acta Arith., 86, 343–383 (1998)

Stephen Choi, K. K., Liu, J. Y.: Small prime solutions of quadratic equations. Canad. J. Math., 54, 71–91 (2002)

Liu, M. C., Tsang, K. M.: On pairs of linear equations in three prime variables and an application to Goldbach’s problem. J. Reine Angew. Math., 399, 109–136 (1989)

Pan, C. D., Pan, C. B.: Goldbach Conjecture, Science Press, Beijing, 1992

Huxley, M. N.: Large values of Dirichlet polynomials (III). Acta Arith., 26, 435–444 (1975)

Jutila, M.: On Linnik’s constant. Math. Scand., 41, 45–62 (1977)

Prachar, K.: Primzahlverteilung, Springer, Berlin, 1957

Davenport, H.: Multiplicative Number Theory, 2nd ed., Springer, Berlin, 1980