Multiple exponential sums with monomials

• Autorzy: Xiaodong Cao , Wenguang Zhai
• Języki publikacji: EN

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints
• 11N45: Asymptotic results on counting functions for algebraic and topological structures
• 11L07: Estimates on exponential sums

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 92
• Numer: 3
• Strony: 195-213

Daty

wydano

2000

otrzymano

1998-08-12

poprawiono

1999-08-30

Twórcy

autor

Xiaodong Cao

• Beijing Institute of Petro-Chemical Technology, Daxing, Beijing, 102600, P.R. China

autor

Wenguang Zhai

• Department of Mathematics, Shandong Normal University, Jinan, Shandong, 250014, P.R. China

Bibliografia

• [1] E. Bombieri and H. Iwaniec, On the order of ζ(1/2+it), Ann. Scuola Norm. Sup. Pisa 13 (1986), 449-472.
• [2] X.-D. Cao and W.-G. Zhai, On the distribution of $p^α$ modulo one, J. Théor. Nombres Bordeaux, to appear.
• [3] X.-D. Cao and W.-G. Zhai, On the distribution of square-full integers, submitted.
• [4] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333.
• [5] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, Cambridge, 1991.
• [6] M. N. Huxley and N. Watt, Exponential sums with a parameter, Proc. London Math. Soc. 59 (1989), 233-252.
• [7] E. Krätzel, Lattice Points, Deutscher Verlag Wiss., Berlin, 1988.
• [8] H.-Q. Liu, On the number of abelian groups of a given order (supplement), Acta Arith. 64 (1993), 285-296.
• [9] P. Sargos and J. Wu, Multiple exponential sums with monomials and their applications in number theory, Acta Math. Hungar. 88 (2000), to appear.
• [10] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Clarendon Press, Oxford, 1951.