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- W2247138283 abstract "One of the most interesting results of Hardy and Littlewood was their Tauberian theorem for Lambert summability [1921]; see Section I.10, or Theorem 12.1 below. This result implies the prime number theorem (PNT), but the proof made use of estimates from number theory somewhat stronger than the PNT! There was another Tauberian-type theorem which implies the PNT and whose state was unsatisfactory. That was Landau’s complex Tauberian theorem [1908], [1909] for Dirichlet series, which required more information about the Riemann zeta function in the half-plane {Re z ≥ 1} than seemed reasonable (see Section III.2)." @default.
- W2247138283 created "2016-06-24" @default.
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- W2247138283 date "2004-01-01" @default.
- W2247138283 modified "2023-10-05" @default.
- W2247138283 title "Wiener’s Theory" @default.
- W2247138283 doi "https://doi.org/10.1007/978-3-662-10225-1_2" @default.
- W2247138283 hasPublicationYear "2004" @default.
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