ArticleOriginal scientific text

Title

On sums of five almost equal prime squares

Authors 1, 1

Affiliations

  1. Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China

Bibliography

  1. F. C. Auluck and S. Chowla, The representation of a large number as a sum of 'almost equal' squares, Proc. Indian Acad. Sci. Sect. A 6 (1937), 81-82.
  2. A. Balog and A. Perelli, Exponential sums over primes in short intervals, Acta Math. Hungar. 48 (1986), 223-228.
  3. H. Davenport, Multiplicative Number Theory, 2nd ed., revised by H. L. Montgomery, Springer, 1980.
  4. A. Ghosh, The distribution of αp² modulo one, Proc. London Math. Soc. (3) 42 (1981), 252-269.
  5. G. Harman, Trigonometric sums over primes I, Mathematika 28 (1981), 249-254.
  6. L.-K. Hua, Some results in the additive prime number theory, Quart. J. Math. 9 (1938), 68-80.
  7. C.-H. Jia, Three prime theorem in short intervals (VII), Acta Math. Sinica 10 (1994), 369-387.
  8. J. Y. Liu and T. Zhan, Estimation of exponential sums over primes in short intervals (I), to appear.
  9. J. Y. Liu and T. Zhan, Estimation of exponential sums over primes in short intervals (II), in: Proceedings of the Halberstam Conference on Analytic Number Theory, Birkhäuser, 1996, to appear.
  10. C. D. Pan and C. B. Pan, On estimations of trigonometric sums over primes in short intervals (III), Chinese Ann. Math. Ser. B 11 (1990), 138-147.
  11. E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., revised by D. R. Heath-Brown, Oxford University Press, 1988.
  12. R. C. Vaughan, An elementary method in prime number theory, in: Recent Progress in Analytic Number Theory, H. Halberstam and C. Hooley (eds.), Academic Press, 1981, 341-348.
  13. I. M. Vinogradov, Estimation of certain trigonometric sums with prime variables, Izv. Akad. Nauk SSSR Ser. Mat. 3 (1939), 371-398 (in Russian).
  14. E. M. Wright, The representation of a number as a sum of three or four squares, Proc. London Math. Soc. 42 (1937), 481-500.
  15. T. Zhan, On the representation of large odd integers as sum of three almost equal primes, Acta Math. Sinica (N.S.) 7 (1991), 159-272.
Pages:
369-383
Main language of publication
English
Received
1996-02-09
Published
1996
Exact and natural sciences