Acta Arithmetica Ix (1964) Arithmetical Tauberian Theorems
نویسنده
چکیده
(1) f(x) = x+o(x) . The problem is discussed explicitly by Landau ([7], pp . 597-604 ; [8]), Ingham ([3]), Karamata ([5], [6]), Gordon ([1]), and is implicit in the 'Eratosthenian' summation method introduced by Wintner ([10], [11]) . In this paper we consider the analogous problem in which the sequence {n} of all positive integers is replaced by a finite or infinite sequence 1, a,, a2, . . . of real numbers for which 1 1<a,<a2< . . . . A=~,-< 00. an
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