On some tauberian theorems related to the prime number theorem
Hildebrand, A. ; Tenenbaum, G.
Compositio Mathematica, Tome 94 (1994), p. 315-349 / Harvested from Numdam
Publié le : 1994-01-01
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     author = {Hildebrand, Adolph and Tenenbaum, G\'erald},
     title = {On some tauberian theorems related to the prime number theorem},
     journal = {Compositio Mathematica},
     volume = {94},
     year = {1994},
     pages = {315-349},
     mrnumber = {1272104},
     zbl = {0804.11052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1994__90_3_315_0}
}
Hildebrand, A.; Tenenbaum, G. On some tauberian theorems related to the prime number theorem. Compositio Mathematica, Tome 94 (1994) pp. 315-349. http://gdmltest.u-ga.fr/item/CM_1994__90_3_315_0/

[Bo1] E. Bombieri, Sull'analogo della formula di Selberg nei corpi di funzioni, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 35 (1963), 252-257. | MR 175885 | Zbl 0121.28201

[Bo2] E. Bombieri, Correction to my paper "Sull'analogo della formula di Selberg nei corpi di funzioni", ibid. (9) 1 (1990), 177-179. | MR 1083245 | Zbl 0714.11060

[De] H. Delange, Sur les fonctions arithmétiques multiplicatives, Ann. Scient. Ec. Norm. Sup. 3° série 78 (1961), 273-304. | Numdam | MR 169829 | Zbl 0234.10043

[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. | MR 33309 | Zbl 0034.31501

[Gr] A. Granville, Solution of a problem of Bombieri, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., to appear. | MR 1250496 | Zbl 0805.11071

[Ha1] G. Halász, Über die Mittelwerte multiplikativer zahlentheorischer Funktionen, Acta Math. Acad. Sci. Hung. 19 (1968), 365-403. | MR 230694 | Zbl 0165.05804

[Ha2] G. Halász, On the distribution of additive and the mean values of multiplicative arithmetic functions, Studia Scient. Math. Hungar. 6 (1971), 211-233. | MR 319930 | Zbl 0226.10046

[HR] H. Halaberstam and H.-E. Richert, On a result of R. R. Hall, J. Number Theory (1) 11 (1979), 76-89. | MR 527762 | Zbl 0395.10048

[Ha] R.R. Hall, Halving an estimate obtained from Selberg's upper bound method, Acta Arith. 25 (1974), 347-351. | MR 340193 | Zbl 0272.10025

[HT] R.R. Hall and G. Tenenbaum, Effective mean value estimates for complex multiplicative functions, Math. Proc. Camb. Phil. Soc. 110 (1991), 337-351. | MR 1113432 | Zbl 0741.11039

[IMW] K.H. Indlekofer, E. Manstavicius, and R. Warlimont, On a certain class of infinite products with an application to arithmetical semigroups, preprint. | MR 1100569 | Zbl 0708.11041

[Mo] H.L. Montgomery, A note on the mean values of multiplicative functions, Inst. Mittag Leffler (1978), Report no 17.

[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, London 1991. | MR 1190927 | Zbl 0744.26011

[MV] H.L. Montgomery and R.C. Vaughan, Mean values of multiplicative functions, preprint. | MR 1830577 | Zbl 0980.11043

[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 de Nancy I (1990), xiv + 499 pp. | MR 1366197 | Zbl 0788.11001

[Wi] E. Wirsing, Das asymptotishe Verhalten von Summen über multiplikative Funktionen II, Acta Math. Acad. Sci. Hung. 18 (1967), 411-467. | MR 223318 | Zbl 0165.05901

[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). | MR 1084200 | Zbl 0723.11047

[Zh2] W.-B. Zhang, Elementary proofs of the abstract prime number theorem for algebraic function fields, Trans. Amer. Math. Soc. 332 (1992), 923-937. | MR 1061781 | Zbl 0759.11030