On the average number of direct factors of finite abelian groups (II)

• Autorzy: Wenguang Zhai
• Języki publikacji: EN

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 1
• Strony: 69-78

Daty

wydano

1999

otrzymano

1998-09-15

poprawiono

1999-01-19

Twórcy

autor

Wenguang Zhai

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

Bibliografia

• [1] E. Cohen, On the average number of direct factors of a finite abelian group, Acta Arith. 6 (1960), 159-173.
• [2] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333.
• [3] D. R. Heath-Brown, The Pjateckiĭ-Šapiro prime number theorem, ibid. 16 (1983), 242-266.
• [4] A. Ivić, The Riemann Zeta-function, Wiley, 1985.
• [5] G. Kolesnik, On the estimation of multiple exponential sums, in: Recent Progress in Analytic Number Theory (Durham, 1979), Vol. 1, Academic Press, London, 1981, 231-246.
• [6] E. Krätzel, On the average number of direct factors of a finite abelian group, Acta Arith. 51 (1988), 369-379.
• [7] H. Q. Liu, Divisor problems of 4 and 3 dimensions, ibid. 73 (1995), 249-269.
• [8] H. Menzer, Vierdimensionale Gitterpunktprobleme I, II, Forschungsergebnisse, FSU, Jena, N/89/38, N/89/02, 1992.
• [9] H. Menzer, On the average number of direct factors of a finite Abelian group, J. Théor. Nombres Bordeaux 7 (1995), 155-164.
• [10] H. Menzer and R. Seibold, On the average number of direct factors of a finite Abelian group, Monatsh. Math. 110 (1990), 63-72.
• [11] S. H. Min, Methods of Number Theory, Science Press, Beijing, 1983 (in Chinese).
• [12] B. R. Srinivasan, The lattice point problem of many-dimensional hyperboloids II, Acta Arith. 8 (1963), 173-204.
• [13] J. Wu, On the average number of unitary factors of finite abelian groups, ibid. 84 (1998), 17-29.
• [14] G. Yu, On the number of direct factors of finite Abelian groups, Acta Math. Sinica 37 (1994), 663-670.
• [15] W. G. Zhai and X. D. Cao, On the average number of direct factors of finite abelian groups, Acta Arith. 82 (1997), 45-55.