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Independence of additive, multiplicative, exponential and logarithmic functions

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Abstract

The independence of four types of functions, namely, additive, multiplicative, exponential and logarithmic functions defined over two types of domains, namely, discrete and non-discrete sets are investigated.

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References

  1. Aczél, J., Dhombres, J.: Functional Equations in Several Variables. Cambridge University Press, Cambridge (1989)

    Book  MATH  Google Scholar 

  2. Apostol, T.M.: Introduction to Analytic Number Theory. Springer, New York (1976)

    Book  MATH  Google Scholar 

  3. Kannappan, Pl: Functional Equations and Inequalities with Applications. Springer, Heidelberg (2009)

    Book  MATH  Google Scholar 

  4. Komatsu, T., Laohakosol, V., Ruengsinsub, P.: Independence measures of arithmetic functions. J. Number Theory 131, 1–17 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lang, S.: Algebra. Addison-Wesley, Reading (1993)

    MATH  Google Scholar 

  6. Ponpetch, K., Laohakosol, V., Mavecha, S.: Linear dependence of four types of arithmetic functions. Songklanakarin J. Sci. Technol (to appear)

  7. Popken, J.: On multiplicative arithmetic functions. In: Studies in Math. Analysis and Related Topics: Essays in Honour of G. Pólya, Stanford University Press, pp. 285–293 (1962)

  8. Reich, L., Schwaiger, J.: Über algebraische relationen zwischen additiven und multiplikativen funktionen. Aequ. Math. 27, 114–134 (1984)

    Article  MATH  Google Scholar 

  9. Reich, L., Schwaiger, J.: On polynomials in additive and multiplicative functions. In: Aczél, J. (ed.) Functional Equations: History, Applications and Theory, pp. 127–160. Reidel, Dordrecht (1984)

    Chapter  Google Scholar 

  10. Schwaiger, J., Prager, W.: Polynomial in additive functions and generalized polynomials. Demonstr. Math. 41(3), 589–613 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Shapiro, H.N., Sparer, G.H.: On algebraic independence of Dirichlet series. Commun. Pure Appl. Math. 39, 695–745 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sivaramakrishnan, R.: Classical Theory of Arithmetic Functions. Marcel Dekker, New York (1989)

    MATH  Google Scholar 

  13. Voorhoeve, M., van der Poorten, A.J.: Wronskian determinants and the zeros of certain functions. Indag. Math. 78(5), 417–424 (1975)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the referee for his thorough reading of the manuscript, his valuable suggestions and his unfailing help.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand

    Kanet Ponpetch & Sukrawan Mavecha

  2. Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand

    Vichian Laohakosol

Authors
  1. Kanet Ponpetch
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  2. Vichian Laohakosol
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  3. Sukrawan Mavecha
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Correspondence to Kanet Ponpetch.

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Ponpetch, K., Laohakosol, V. & Mavecha, S. Independence of additive, multiplicative, exponential and logarithmic functions. Aequat. Math. 93, 875–904 (2019). https://doi.org/10.1007/s00010-019-00648-7

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  • DOI: https://doi.org/10.1007/s00010-019-00648-7

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