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

Hong-Quan Liu

Acta Arithmetica (1999)

  • Volume: 90, Issue: 4, page 357-370
  • ISSN: 0065-1036

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Hong-Quan Liu. "On a fundamental result in van der Corput's method of estimating exponential sums." Acta Arithmetica 90.4 (1999): 357-370. <http://eudml.org/doc/207333>.

@article{Hong1999,
author = {Hong-Quan Liu},
journal = {Acta Arithmetica},
keywords = {estimates on exponential sums; van der Corput method; error term},
language = {eng},
number = {4},
pages = {357-370},
title = {On a fundamental result in van der Corput's method of estimating exponential sums},
url = {http://eudml.org/doc/207333},
volume = {90},
year = {1999},
}

TY - JOUR
AU - Hong-Quan Liu
TI - On a fundamental result in van der Corput's method of estimating exponential sums
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 4
SP - 357
EP - 370
LA - eng
KW - estimates on exponential sums; van der Corput method; error term
UR - http://eudml.org/doc/207333
ER -

References

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  5. [5] G. Kolesnik, On the order of ζ(1/2 + it) and Δ(R), Pacific J. Math. 98 (1982), 107-122. Zbl0476.10032
  6. [6] H.-Q. Liu, On the number of abelian groups of a given order, Acta Arith. 59 (1991), 261-277. Zbl0737.11024
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  9. [9] H.-Q. Liu, The number of cube-full numbers in an interval, Acta Arith.. 67 (1994), 1-12. 
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  14. [14] H.-Q. Liu, Almost primes in short intervals, J. Number Theory 57 (1996), 301-322. Zbl0847.11045
  15. [15] H.-Q. Liu and J. Rivat, On the Pjateckiĭ-Šapiro prime number theorem, Bull. London Math. Soc. 24 (1992), 143-147. Zbl0772.11032
  16. [16] S. H. Min, Methods in Number Theory, Vol. 2, Science Press, 1981 (in Chinese). Zbl0649.10001
  17. [17] E. Phillips, The zeta-function of Riemann, further developments of van der Corput's method, Quart. J. Math. 4 (1933), 209-225. Zbl59.0204.01
  18. [18] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., revised by D. R. Heath-Brown, Oxford, 1986. Zbl0601.10026
  19. [19] J. Wu, On the average number of unitary factors of finite abelian groups, Acta Arith. 84 (1998), 17-29. 
  20. [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. 

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