Skip to main content
SpringerLink
Log in

Some estimates in the theory of exponential sums

  • Published:
Acta Mathematica Academiae Scientiarum Hungarica Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. N. G. de Bruijn, On Turán's first main theorem,Acta Math. Acad. Sci. Hung.,11 (1960), pp. 213–216.

    Google Scholar 

  2. I. Dancs, On an extremal problem,Acta Math. Acad. Sci. Hung.,9 (1958), pp. 309–313.

    Google Scholar 

  3. I. Dancs, On generalized sums of powers of complex numbers,Ann. Univ. Sci. Budapest Eötvös, Sect. Math.,7 (1964), pp. 113–121.

    Google Scholar 

  4. J. M. Geysel, On generalized sums of powers of complex numbers, M. C. Report Z. W. 1968-013, Math. Centr. (Amsterdam, 1968).

    Google Scholar 

  5. E. Makai, The first main theorem of P. Turán,Acta Math. Acad. Sci. Hung.,10 (1959), pp. 405–411.

    Google Scholar 

  6. E. Makai, On a minimumproblem,Ann. Univ. Sci. Budapest Eötvös, Sect. Math.,3–4 (1960–61), pp. 177–182.

    Google Scholar 

  7. E. Makai, On a minimumproblem. II,Acta Math. Acad. Sci. Hung.,15 (1964), pp. 63–66.

    Google Scholar 

  8. G. Pólya andG. Szegő,Aufgaben und Lehrsätze aus der Analysis; Springer (Berlin, 1964).

    Google Scholar 

  9. A. J. van der Poorten,Simultaneous algebraic approximation of functions, Ph. D. Thesis, Univ. of N.S.W. (Australia, 1968).

    Google Scholar 

  10. A. J. van der Poorten, Generalizations of Turán's main theorems on lower bounds for sums of powers,Bull. Austral. Math. Soc.,2 (1970), pp. 15–37.

    Google Scholar 

  11. V. T. Sós andP. Turán, On some new theorems in the theory of Diophantine approximations,Acta Math. Acad. Sci. Hung.,6 (1955), pp. 241–255.

    Google Scholar 

  12. R. Tijdeman,On the distribution of the values of certain functions, Thesis, Univ. of Amsterdam (The Netherlands, 1969).

    Google Scholar 

  13. R. Tijdeman, On the number of zeros of general exponential polynomials,Indag. Math.,33 (1971), pp. 1–7.

    Google Scholar 

  14. R. Tijdeman, An auxiliary result in the theory of transcendental numbers,J. Number Theory (to appear).

  15. P. Turán,Eine neue Methode in der Analysis und deren Anwendungen, Akad. Kiadó, (Budapest, 1953). A chinese edition appeared in 1956.

    Google Scholar 

  16. S. Uchiyama, A note on the second main theorem of P. Turán,Acta Math. Acad. Sci. Hung.,9, (1958), pp. 379–380.

    Google Scholar 

  17. E. T. Whittaker andG. N. Watson,A course of modern analysis: Cambridge Univ. Press., 1969.

  18. P. Turán, Diophantine approximation and analysis, Actes, Congrès intern. math., 1970, Gauthiers-Villars, Tome 1, pp. 519–528 (in particular p. 527).

Download references

Author information

Authors and Affiliations

  1. Mathematisch Instituut, Roetersstraat 15, Amsterdam, The Netherlands

    A. A. Balkema

  2. Mathematisch Instituut, Wassenaarseweg 80, Leiden, The Netherlands

    R. Tijdeman

Authors
  1. A. A. Balkema
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Tijdeman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Balkema, A.A., Tijdeman, R. Some estimates in the theory of exponential sums. Acta Mathematica Academiae Scientiarum Hungaricae 24, 115–133 (1973). https://doi.org/10.1007/BF01894619

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01894619

Search

Navigation