On some tauberian theorems related to the prime number theorem

A. Hildebrand; G. Tenenbaum

Compositio Mathematica (1994)

  • Volume: 90, Issue: 3, page 315-349
  • ISSN: 0010-437X

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Hildebrand, A., and Tenenbaum, G.. "On some tauberian theorems related to the prime number theorem." Compositio Mathematica 90.3 (1994): 315-349. <http://eudml.org/doc/90277>.

@article{Hildebrand1994,
author = {Hildebrand, A., Tenenbaum, G.},
journal = {Compositio Mathematica},
keywords = {asymptotic behaviour of sequences; Tauberian theorems; mean value; prime number theorem},
language = {eng},
number = {3},
pages = {315-349},
publisher = {Kluwer Academic Publishers},
title = {On some tauberian theorems related to the prime number theorem},
url = {http://eudml.org/doc/90277},
volume = {90},
year = {1994},
}

TY - JOUR
AU - Hildebrand, A.
AU - Tenenbaum, G.
TI - On some tauberian theorems related to the prime number theorem
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 90
IS - 3
SP - 315
EP - 349
LA - eng
KW - asymptotic behaviour of sequences; Tauberian theorems; mean value; prime number theorem
UR - http://eudml.org/doc/90277
ER -

References

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  2. [Bo2] E. Bombieri, Correction to my paper "Sull'analogo della formula di Selberg nei corpi di funzioni", ibid. (9) 1 (1990), 177-179. Zbl0714.11060MR1083245
  3. [De] H. Delange, Sur les fonctions arithmétiques multiplicatives, Ann. Scient. Ec. Norm. Sup.3° série 78 (1961), 273-304. Zbl0234.10043MR169829
  4. [Er] P. Erdös, On a Tauberian theorem connected with the new proof of the prime number theorem, J. Indian Math. Soc.13 (1949), 131-147. Zbl0034.31501MR33309
  5. [Gr] A. Granville, Solution of a problem of Bombieri, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., to appear. Zbl0805.11071MR1250496
  6. [Ha1] G. Halász, Über die Mittelwerte multiplikativer zahlentheorischer Funktionen, Acta Math. Acad. Sci. Hung.19 (1968), 365-403. Zbl0165.05804MR230694
  7. [Ha2] G. Halász, On the distribution of additive and the mean values of multiplicative arithmetic functions, Studia Scient. Math. Hungar.6 (1971), 211-233. Zbl0226.10046MR319930
  8. [HR] H. Halaberstam and H.-E. Richert, On a result of R. R. Hall, J. Number Theory (1) 11 (1979), 76-89. Zbl0395.10048MR527762
  9. [Ha] R.R. Hall, Halving an estimate obtained from Selberg's upper bound method, Acta Arith.25 (1974), 347-351. Zbl0272.10025MR340193
  10. [HT] R.R. Hall and G. Tenenbaum, Effective mean value estimates for complex multiplicative functions, Math. Proc. Camb. Phil. Soc.110 (1991), 337-351. Zbl0741.11039MR1113432
  11. [IMW] K.H. Indlekofer, E. Manstavicius, and R. Warlimont, On a certain class of infinite products with an application to arithmetical semigroups, preprint. Zbl0708.11041MR1100569
  12. [Mo] H.L. Montgomery, A note on the mean values of multiplicative functions, Inst. Mittag Leffler (1978), Report no 17. 
  13. [MPF] D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Inequalities Involving Functions, and their Integrals and Derivatives, Math. and its Appl., Vol. 53, Kluwer, Dordrecht, Boston, London1991. Zbl0744.26011MR1190927
  14. [MV] H.L. Montgomery and R.C. Vaughan, Mean values of multiplicative functions, preprint. Zbl0980.11043MR1830577
  15. [Te] G. Tenenbaum, Introduction à la Théorie Analytique et Probabiliste des Nombres, Revue de l'Institut Elie Cartan 13, Département de Mathématiques de l'Université deNancy I (1990), xiv + 499 pp. Zbl0788.11001MR1366197
  16. [Wi] E. Wirsing, Das asymptotishe Verhalten von Summen über multiplikative Funktionen II, Acta Math. Acad. Sci. Hung.18 (1967), 411-467. Zbl0165.05901MR223318
  17. [Zh1] W.-B. Zhang, The abstract prime number theorem for algebraic function fields, in: B. Berndt, H. Diamond, H. Halberstam, and A. Hildebrand (eds.), Analytic Number Theory (Urbana, 1989), Prog. Math.85, 529-558 (Birkhäuser, 1990). Zbl0723.11047MR1084200
  18. [Zh2] W.-B. Zhang, Elementary proofs of the abstract prime number theorem for algebraic function fields, Trans. Amer. Math. Soc.332 (1992), 923-937. Zbl0759.11030MR1061781

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