Functiones et Approximatio Commentarii Mathematici

Multiplicative function mean values: asymptotic estimates

Peter D.T.A. Elliott

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Abstract

Classical Mean-Value results of Wirsing type are established under weaker than classical constraints.

Article information

Source
Funct. Approx. Comment. Math., Volume 56, Number 2 (2017), 217-238.

Dates
First available in Project Euclid: 28 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1490688012

Digital Object Identifier
doi:10.7169/facm/1608

Mathematical Reviews number (MathSciNet)
MR3660961

Zentralblatt MATH identifier
06864156

Subjects
Primary: 11N37: Asymptotic results on arithmetic functions
Secondary: 11N56: Rate of growth of arithmetic functions 11N60: Distribution functions associated with additive and positive multiplicative functions 94A17: Measures of information, entropy

Keywords
multiplicative function mean value Maass form

Citation

Elliott, Peter D.T.A. Multiplicative function mean values: asymptotic estimates. Funct. Approx. Comment. Math. 56 (2017), no. 2, 217--238. doi:10.7169/facm/1608. https://projecteuclid.org/euclid.facm/1490688012


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References

  • M.B. Barban, The “Large Sieve” method and its application in the Theory of Numbers (Russian), Uspekhi Mat. Nauk 21 (1966), no. 1(127), 51–102, English version in Russian Math. Surveys 21 (1966), no. 1, 41–103.
  • N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular variation, Encyclopedia of Mathematics and its Applications, vol. 27, Cambridge University Press, Cambridge, 1987.
  • H. Delange, Sur les fonctions arithmétiques multiplicatives et ses applications, Ann. Sci. École Norm. Sup. (3) 78 (1961), no. 1, 1–29.
  • P.D.T.A. Elliott, Extrapolating the mean-values of multiplicative functions, Indag. Math. 92 (1989), no. 4, 409–420, originally Nederl. Akad. Wetensch. Proc. Ser. A
  • P.D.T.A. Elliott, Duality in analytic number theory, Cambridge Tracts in Mathematics, vol. 122, Cambridge University Press, Cambridge, 1997.
  • P.D.T.A. Elliott and J. Kish, Harmonic analysis on the positive rationals I: Basic results, J. Fac. Sci. Univ. Tokyo 23 (2016), no. 3, see also arXiv:1405.7130.
  • P.D.T.A. Elliott and J. Kish, Harmonic analysis on the positive rationals II: Multiplicative functions and Maass forms, J. Math. Sci. Univ. Tokyo 23 (2016), no. 3, see also arXiv:1405.7132.
  • W. Feller, On the classical Tauberian theorems, Arch. Math. 14 (1963), no. 1, 317–322.
  • G. Halász, Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar. 19 (1968), 365–403.
  • K.-H. Indlekofer, R. Wagner, and I. Kátai, A comparative result for multiplicative functions, Lithuanian Math. J. 41 (2001), no. 2, 143–157.
  • J. Korevaar, Tauberian theory: A century of developments, Grundlehren der mathematischen Wissenschaften, vol. 329, Springer-Verlag, 2004.
  • U. Stadtmüller and R. Trautner, Tauberian theorems for Laplace transforms, J. reine angew. Math. 311/312 (1979), 283–290.
  • E. Wirsing, Das asymptotische Verhalten von Summen über multiplikative Funktionen, Math. Ann. 143 (1961), 75–102.
  • E. Wirsing, Das asymptotische Verhalten von Summen über multiplikative Funktionen. II, Acta Math. Acad. Sci. Hungar. 18 (1967), 411–467.