Download PDF - On a fundamental result in van der Corput's method of estimating exponential sumsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On a fundamental result in van der Corput's method of estimating exponential sums

Authors 1

Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150006, China

Bibliography

  1. L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1966.
  2. R. C. Baker and G. Harman, Numbers with a large prime factor, Acta Arith. 73 (1995), 119-145.
  3. D. R. Heath-Brown, The Pjateckiĭ-Šapiro prime number theorem, J. Number Theory 16 (1983), 242-266.
  4. C. H. Jia, The distribution of squarefree numbers, Sci. China Ser. A 36 (1993), 154-169.
  5. G. Kolesnik, On the order of ζ(1/2 + it) and Δ(R), Pacific J. Math. 98 (1982), 107-122.
  6. H.-Q. Liu, On the number of abelian groups of a given order, Acta Arith. 59 (1991), 261-277.
  7. H.-Q. Liu, On the number of abelian groups of a given order (supplement), Acta Arith.. 64 (1993), 285-296.
  8. H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith.. 65 (1993), 301-328.
  9. H.-Q. Liu, The number of cube-full numbers in an interval, Acta Arith.. 67 (1994), 1-12.
  10. H.-Q. Liu, The distribution of 4-full numbers, Acta Arith.. 67 (1994), 165-176.
  11. H.-Q. Liu, On some divisor problems, Acta Arith.. 68 (1994), 193-200.
  12. H.-Q. Liu, Divisor problems of 4 and 3 dimensions, Acta Arith.. 73 (1995), 249-269.
  13. H.-Q. Liu, A special triple exponential sum, Mathematika 42 (1995), 137-143.
  14. H.-Q. Liu, Almost primes in short intervals, J. Number Theory 57 (1996), 301-322.
  15. H.-Q. Liu and J. Rivat, On the Pjateckiĭ-Šapiro prime number theorem, Bull. London Math. Soc. 24 (1992), 143-147.
  16. S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1981 (in Chinese).
  17. E. Phillips, The zeta-function of Riemann, further developments of van der Corput's method, Quart. J. Math. 4 (1933), 209-225.
  18. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., revised by D. R. Heath-Brown, Oxford, 1986.
  19. J. Wu, On the average number of unitary factors of finite abelian groups, Acta Arith. 84 (1998), 17-29.
  20. W.-G. Zhai and X.-D. Cao, On the average number of direct factors of finite abelian groups, Acta Arith.. 82 (1997), 45-55.
Acta Arithmetica
1999/90/4
Export to PBN, Opens in new tab
Pages:
357-370
Main language of publication
English
Received
1998-09-15
Accepted
1999-05-04
Published
1999
Exact and natural sciences