Functiones et Approximatio Commentarii Mathematici

On the average number of unitary factors of finite abelian groups

H.-Q. Liu

Full-text: Open access

Abstract

We give a slight improvement on a well-known problem.

Article information

Source
Funct. Approx. Comment. Math., Volume 43, Number 1 (2010), 7-14.

Dates
First available in Project Euclid: 28 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1285679141

Digital Object Identifier
doi:10.7169/facm/1285679141

Mathematical Reviews number (MathSciNet)
MR2683569

Zentralblatt MATH identifier
1278.11093

Subjects
Primary: 11L06
Secondary: 11N45: Asymptotic results on counting functions for algebraic and topological structures

Keywords
exponential sums abelian groups

Citation

Liu, H.-Q. On the average number of unitary factors of finite abelian groups. Funct. Approx. Comment. Math. 43 (2010), no. 1, 7--14. doi:10.7169/facm/1285679141. https://projecteuclid.org/euclid.facm/1285679141


Export citation

References

  • E.Bombieri, On the large sieve, Mathematika 12 (1965), 201--225.
  • E. Kratzel, On the average number of direct factors of a finite abelian groups, Acta Arith. 51 (1988), 369--379.
  • H.-Q.Liu, On some divisor problems, ibid, 68 (1994), 193--200.
  • H.-Q.Liu, Divisors problems of 4 and 3 dimensions, ibid, 73 (1995), 249--269.
  • H.-Q.Liu, On the estimates for double exponential sums, ibid, 129 (2007), 203--247.
  • S.H.Min, On the order of $\zeta\left(\frac12+it\right)$, Trans. Amer. Math. Soc. 65 (1949), 448--472.
  • M.Redouaby et P.Sargos, Sur la transformation B de Van der Corput, Expositiones Math. 17 (1999), no.3, 207--232.
  • P.G.Schmidt, Zur Anzahl unitarer Factoren abelscher Grupppen, Acta Arith. 64 (1993), 237--248.
  • P.Sargos and J.Wu, Multiple exponential sums with monomials and their applications in number theory, Acta Math. Hungar. 87 (2000), 333--354.
  • J.Wu, On the average number of unitary factors of finite abelian groups, Acta Arith. 84 (1998), 17--29.
  • J.Wu, Double exponential sums and some applications, Mh. Math. 128 (1999), 255--262.