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

Acta Arithmetica

Volumn 90, Issue 4, 1999, Pages 357-370

  Liu, Hong Quan ^a,b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b NONE   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033261146     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-90-4-357-370     Document Type: Article

References (20)

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4. C. H. Jia, The distribution of squarefree numbers, Sci. China Ser. A 36 (1993), 154-169.
5. G. Kolesnik, On the order of ς(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. _, On the number of abelian groups of a given order (supplement), ibid. 64 (1993), 285-296.
8. _, The greatest prime factor of the integers in an interval, ibid. 65 (1993), 301-328.
9. _, The number of cube-full numbers in an interval, ibid. 67 (1994), 1-12.
10. _, The distribution of 4-full numbers, ibid. 67 (1994), 165-176.
11. _, On some divisor problems, ibid. 68 (1994), 193-200.
12. _, Divisor problems of 4 and 3 dimensions, ibid. 73 (1995), 249-269.
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14. _, Almost primes in short intervals, J. Number Theory 57 (1996), 301-322.
15. H.-Q. Liu and J. Rivat, On the Pjateckiǐ-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, ibid. 82 (1997), 45-55.