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New estimates in the four-dimensional divisor problem with applications

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Abstract

In this article we consider three problems: 1. The asymptotic behaviour of the quadratic moment of the exponential divisor function. 2. The distribution of powerful integers of type 4. 3. The average number of direct factors of a finite Abelian group. We prove new estimates for the error terms in the asymptotic representations. For this purpose new estimates in the general four-dimensional divisor problem are needed.

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References

  1. E. Cohen, On the average number of direct factors of a finite abelian group, Acta Arith., 6 (1960), 159–173.

    MATH  MathSciNet  Google Scholar 

  2. E. Krätzel, Lattice Points, Dt. Verlag d. Wiss. (Berlin) and Kluwer Academic Publishers (Dordrecht — Boston — London, 1988).

    MATH  Google Scholar 

  3. E. Krätzel, On the average number of direct factors of a finite abelian group, Acta Arith., 51 (1988), 369–379.

    MATH  MathSciNet  Google Scholar 

  4. E. Krätzel, The distribution of powerful integers of type 4, Acta Arith., 52 (1989), 141–145.

    MATH  MathSciNet  Google Scholar 

  5. E. Krätzel, Estimates in the general divisor problem, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 191–206.

    Article  MATH  MathSciNet  Google Scholar 

  6. E. Krätzel, The distribution of values of the enumerating function of finite, non-isomorphic Abelian groups in short intervals, Archiv Math., 91 (2008), 518–525.

    Article  MATH  Google Scholar 

  7. E. Krätzel, The four-dimensional divisor problem, Uniform Distribution Theory, 3 (2009), 93–103.

    Google Scholar 

  8. R. Seibold und E. Krätzel, Exponentialsummen und unsymmetrische Teilerprobleme, Analysis, 18 (1998), 201–215.

    MATH  Google Scholar 

  9. M. Vogts, Many-dimensional generalized divisor problems, Math. Nachr,. 124 (1985), 103–121.

    Article  MATH  MathSciNet  Google Scholar 

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  1. Institut für Mathematik, Universität Wien, Nordbergstr. 15, A-1090, Wien, Austria

    E. Krätzel

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  1. E. Krätzel
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Krätzel, E. New estimates in the four-dimensional divisor problem with applications. Acta Math Hung 126, 258–278 (2010). https://doi.org/10.1007/s10474-009-9059-0

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  • DOI: https://doi.org/10.1007/s10474-009-9059-0

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