On the average number of unitary factors of finite abelian groups

• Autorzy: J. Wu
• Języki publikacji: EN

Kategorie tematyczne

• 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: 1998
• Tom: 84
• Numer: 1
• Strony: 17-29

Daty

wydano

1998

otrzymano

1996-11-29

poprawiono

1997-10-30

Twórcy

autor

J. Wu

• Laboratoire de Mathématiques, Institut Élie Cartan - CNRS UMR 9973, Université Henri Poincaré (Nancy 1), 54506 Vandœ uvre-lès-Nancy, France

Bibliografia

• [1] R. C. Baker and G. Harman, Numbers with a large prime factor, Acta Arith. 73 (1995), 119-145.
• [2] E. Cohen, On the average number of direct factors of a finite abelian group, Acta Arith. 6 (1960), 159-173.
• [3] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333.
• [4] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, Cambridge Univ. Press, Cambridge, 1991.
• [5] C. H. Jia, The distribution of square-free numbers, Sci. China Ser. A 36 (1993), 154-169.
• [6] G. Kolesnik, On the number of abelian groups of a given order, J. Reine Angew. Math. 329 (1981), 164-175.
• [7] E. Krätzel, On the average number of direct factors of a finite abelian group, Acta Arith. 51 (1988), 369-379.
• [8] H.-Q. Liu, The greatest prime factor of the integers in an interval, Acta Arith. 65 (1993), 302-328.
• [9] H.-Q. Liu, On some divisor problems, Acta Arith. 68 (1994), 193-200.
• [10] H.-Q. Liu, Divisor problems of 4 and 3 dimensions, Acta Arith. 73 (1995), 249-269.
• [11] P. G. Schmidt, Zur Anzahl unitärer Faktoren abelscher Gruppen, Acta Arith. 64 (1993), 237-248.
• [12] P. Sargos and J. Wu, Multiple exponential sums with monomials and their applications in number theory, Prépublications 97/n°37 de l'Institut Élie Cartan, Université Henri Poincaré (Nancy 1).
• [13] J. Wu, On the distribution of square-full and cube-full integers, Monatsh. Math., to appear.