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Ramanujan expansions revisited

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References

  1. R. D. Carmichael, Expansions of arithmetical functions in infinite series. Proc. London Math. Soc. (2)34, 1–26 (1932).

    Google Scholar 

  2. E. Cohen, Almost even functions of finite abelian groups. Acta Arith.7, 311–323 (1962).

    Google Scholar 

  3. J. Delsarte, Essai sur l'application de la théorie des fonctions presque-périodiques à l'arithmétique. Ann. Sci. École Norm. Sup.62, 185–204 (1945).

    Google Scholar 

  4. P. D. T. A. Elliott, A mean value theorem for multiplicative functions. Proc. London Math. Soc. (3)3, 418–438 (1975).

    Google Scholar 

  5. G. H. Hardy, Note on Ramanujan's trigonometrical functionsc q(n) and certain series of arithmetical functions. Proc. Cambridge Philos. Soc.20, 263–271 (1921).

    Google Scholar 

  6. A. Hildebrand, Über die punktweise Konvergenz von Ramanujan-Entwicklungen zahlentheoretischer Funktionen. Acta Arith.44, 109–140 (1984).

    Google Scholar 

  7. A. Hildebrand andJ. Spilker, Charakterisierung der additiven, fastgeraden Funktionen. Manuscripta Math.32, 213–230 (1980).

    Google Scholar 

  8. K.-H. Indlekover, A mean-value theorem for multiplicative functions. Math. Z.172, 255–271 (1980).

    Google Scholar 

  9. J.Knopfmacher, Abstract analytic number theory. New York 1975.

  10. E.Landau, Handbuch der Lehre von der Verteilung der Primzahlen. Reprint, 2nd Edition. New York 1953.

  11. L.Lucht, Weighted relationship theorems and Ramanujan expansions. Acta Arith., to appear.

  12. L. Lucht andF. Tuttas, Mean-values of multiplicative functions and natural boundaries of power series with multiplicative coefficients. J. London Math. Soc. (2)19, 25–34 (1979).

    Google Scholar 

  13. S. Ramanujan, On certain trigonometrical sums and their applications in the theory of numbers. Trans. Cambridge Philos. Soc.22, 259–276 (1918).

    Google Scholar 

  14. W. Schwarz, Ramanujan-Entwicklungen stark multiplikativer zahlentheoretischer Funktionen. Acta Arith.22, 329–338 (1973).

    Google Scholar 

  15. W. Schwarz, Ramanujan-Entwicklung stark multiplikativer Funktionen. J. Reine Angew. Math.262/263, 66–73 (1973).

    Google Scholar 

  16. W. Schwarz, Die Ramanujan-Entwicklung reellwertiger multiplikativer Funktionen vom Betrage kleiner oder gleich Eins. J. Reine Angew. Math.271, 171–176 (1974).

    Google Scholar 

  17. W. Schwarz, Über die Ramanujan-Entwicklung multiplikativer Funktionen. Acta Arith.27, 269–279 (1975).

    Google Scholar 

  18. W. Schwarz andJ. Spilker, Eine Anwendung des Approximationssatzes von Weierstrass-Stone auf Ramanujan-Summen. Nieuw Arch. Wisk. (3)19, 198–209 (1971).

    Google Scholar 

  19. W. Schwarz andJ. Spilker, Mean values and Ramanujan expansions of almost even arithmetical functions. In: Proc. 1974 Colloqu. on Number Theory, Debrecen. Colloq. Math. Soc. János Bolyai13, 315–357 (1974).

    Google Scholar 

  20. W.Schwarz and J.Spilker, Arithmetical functions. London Math. Soc. Lecture Notes Series184, Cambridge 1994.

  21. F. Tuttas, Über die Entwicklung multiplikativer Funktionen nach Ramanujan-Summen. Acta Arith.36, 257–270 (1980).

    Google Scholar 

  22. R. Warlimont, Ramanujan expansions of multiplicative functions. Acta Arith.42, 111–120 (1983).

    Google Scholar 

  23. A.Wintner, Eratosthenian averages. Baltimore 1944.

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Dedicated to Wolfgang Schwarz on the occasion of his sixtieth birthday

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Lucht, L. Ramanujan expansions revisited. Arch. Math 64, 121–128 (1995). https://doi.org/10.1007/BF01196630

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  • DOI: https://doi.org/10.1007/BF01196630

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