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

Acta Arithmetica (1999)

- Volume: 90, Issue: 1, page 69-78
- ISSN: 0065-1036

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topWenguang Zhai. "On the average number of direct factors of finite abelian groups (II)." Acta Arithmetica 90.1 (1999): 69-78. <http://eudml.org/doc/207315>.

@article{WenguangZhai1999,

author = {Wenguang Zhai},

journal = {Acta Arithmetica},

keywords = {divisor functions; number of finite abelian groups; asymptotic behaviour; exponential sums},

language = {eng},

number = {1},

pages = {69-78},

title = {On the average number of direct factors of finite abelian groups (II)},

url = {http://eudml.org/doc/207315},

volume = {90},

year = {1999},

}

TY - JOUR

AU - Wenguang Zhai

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

JO - Acta Arithmetica

PY - 1999

VL - 90

IS - 1

SP - 69

EP - 78

LA - eng

KW - divisor functions; number of finite abelian groups; asymptotic behaviour; exponential sums

UR - http://eudml.org/doc/207315

ER -

## References

top- [1] E. Cohen, On the average number of direct factors of a finite abelian group, Acta Arith. 6 (1960), 159-173. Zbl0113.25305
- [2] E. Fouvry and H. Iwaniec, Exponential sums with monomials, J. Number Theory 33 (1989), 311-333. Zbl0687.10028
- [3] D. R. Heath-Brown, The Pjateckiĭ-Šapiro prime number theorem, ibid. 16 (1983), 242-266. Zbl0513.10042
- [4] A. Ivić, The Riemann Zeta-function, Wiley, 1985. Zbl0556.10026
- [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. Zbl0633.10044
- [7] H. Q. Liu, Divisor problems of 4 and 3 dimensions, ibid. 73 (1995), 249-269. Zbl0846.11056
- [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. Zbl0840.11038
- [10] H. Menzer and R. Seibold, On the average number of direct factors of a finite Abelian group, Monatsh. Math. 110 (1990), 63-72. Zbl0731.11054
- [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. Zbl0118.28201
- [13] J. Wu, On the average number of unitary factors of finite abelian groups, ibid. 84 (1998), 17-29. Zbl0899.11048
- [14] G. Yu, On the number of direct factors of finite Abelian groups, Acta Math. Sinica 37 (1994), 663-670. Zbl0820.11056
- [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. Zbl0886.11054

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