@article{CM_1994__90_3_315_0, 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] 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] 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] Sur les fonctions arithmétiques multiplicatives, Ann. Scient. Ec. Norm. Sup. 3° série 78 (1961), 273-304. | Numdam | MR 169829 | Zbl 0234.10043
,[Er] 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] Solution of a problem of Bombieri, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., to appear. | MR 1250496 | Zbl 0805.11071
,[Ha1] Über die Mittelwerte multiplikativer zahlentheorischer Funktionen, Acta Math. Acad. Sci. Hung. 19 (1968), 365-403. | MR 230694 | Zbl 0165.05804
,[Ha2] 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] On a result of R. R. Hall, J. Number Theory (1) 11 (1979), 76-89. | MR 527762 | Zbl 0395.10048
and ,[Ha] Halving an estimate obtained from Selberg's upper bound method, Acta Arith. 25 (1974), 347-351. | MR 340193 | Zbl 0272.10025
,[HT] Effective mean value estimates for complex multiplicative functions, Math. Proc. Camb. Phil. Soc. 110 (1991), 337-351. | MR 1113432 | Zbl 0741.11039
and ,[IMW] On a certain class of infinite products with an application to arithmetical semigroups, preprint. | MR 1100569 | Zbl 0708.11041
, , and ,[Mo] A note on the mean values of multiplicative functions, Inst. Mittag Leffler (1978), Report no 17.
,[MPF] Inequalities Involving Functions, and their Integrals and Derivatives, Math. and its Appl., Vol. 53, Kluwer, Dordrecht, Boston, London 1991. | MR 1190927 | Zbl 0744.26011
, , and ,[MV] Mean values of multiplicative functions, preprint. | MR 1830577 | Zbl 0980.11043
and ,[Te] 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] Das asymptotishe Verhalten von Summen über multiplikative Funktionen II, Acta Math. Acad. Sci. Hung. 18 (1967), 411-467. | MR 223318 | Zbl 0165.05901
,[Zh1] 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] 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
,