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

• Autorzy: Hong-Quan Liu
• Języki publikacji: EN

Kategorie tematyczne

• 11L26: Sums over arbitrary intervals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 4
• Strony: 357-370

Daty

wydano

1999

otrzymano

1998-09-15

poprawiono

1999-05-04

Twórcy

autor

Hong-Quan Liu

• Department of Mathematics, Harbin Institute of Technology, Harbin, 150006, China

Bibliografia

• [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.