Skip to main content
Log in

On the linear combination of q-additive functions at prime places

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Necessary and sufficient conditions are given for linear combinations of q-ary additive functions to belong to some function classes when the summation is extended to the set of primes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. K.-H. Indlekofer and I. Kátai, Investigations in the theory of q-additive and q-multiplicative functions. I, Acta Math. Hungar., 91 (2001), 53–78.

    Article  MATH  MathSciNet  Google Scholar 

  2. K.-H. Indlekofer and I. Kátai, Investigations in the theory of q-additive and q-multiplicative functions. II, Acta Math. Hungar., 97 (2002), 97–108.

    Article  MATH  MathSciNet  Google Scholar 

  3. K.-H. Indlekofer and I. Kátai, On linear combinations of q-additive functions, Annales Univ. Sci. Budapest, Sect. Comp., 21 (2002), 195–208.

    MATH  Google Scholar 

  4. I. Kátai, Distribution of q-additive functions, in: Probability Theory and Applications (eds. J. Galambos and I. Kátai) in the series Mathematics and its Applications, Kluwer Academic Publishers, pp. 309–318.

  5. I. Kátai, Distribution of digits of primes in q-ary canonical form, Acta Math. Hungar., 47 (1986), 341–359.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Coquet, On a result of I. Kátai, Sitzungsberichte der Mathem. Naturw., Kl. Abt. II. Bd. 1–3. Heft 1–11.

  7. P. Erdős and P. Turán, On a problem in the theory of uniform distribution I, Indag. Math., 10 (1948), 370–378.

    Google Scholar 

  8. N. L. Bassily and I. Kátai, Distribution of the values of q-additive functions on polynomial sequences, Acta Math. Hungar., 68 (1995), 353–361.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Selberg, On the normal density of primes in small intervals and the difference between consecutive primes, Arch. Math. Naturvid., 47 (1943), 87–105.

    MathSciNet  Google Scholar 

  10. L.-K. Hua, Additive Theory of Prime Numbers, Translations of Mathematical Monographs Vol. 13., Amer. Math. Soc. (Providence, 1965).

    MATH  Google Scholar 

  11. J. Galambos, Advanced Probability Theory, Marcel Dekker, Inc. (New York, 1988).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. Kátai.

Additional information

Supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA T46993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kátai, I. On the linear combination of q-additive functions at prime places. Acta Math Hung 117, 361–372 (2007). https://doi.org/10.1007/s10474-007-6125-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-007-6125-3

Key words and phrases

2000 Mathematics Subject Classification

Navigation