A Tauberian Theorem and Analogues of the Prime Number Theorem
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 362-367
Voir la notice de l'article provenant de la source Cambridge University Press
In 1945 Ingham (3) proved the following Tauberian theorem: if ƒ is a non-decreasing, non-negative function on [1, ∞) and 1 then ƒ(x) ∼ cx. His proof is based on the non-vanishing of the Riemann zeta-function, ζ (s), on the line , and uses Pitt's form of Wiener's Tauberian theorem; (see, e.g., 5, Theorem 109, p. 211).
Davison, T. M. K. A Tauberian Theorem and Analogues of the Prime Number Theorem. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 362-367. doi: 10.4153/CJM-1968-032-2
@article{10_4153_CJM_1968_032_2,
author = {Davison, T. M. K.},
title = {A {Tauberian} {Theorem} and {Analogues} of the {Prime} {Number} {Theorem}},
journal = {Canadian journal of mathematics},
pages = {362--367},
year = {1968},
volume = {20},
number = {1},
doi = {10.4153/CJM-1968-032-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-032-2/}
}
TY - JOUR AU - Davison, T. M. K. TI - A Tauberian Theorem and Analogues of the Prime Number Theorem JO - Canadian journal of mathematics PY - 1968 SP - 362 EP - 367 VL - 20 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-032-2/ DO - 10.4153/CJM-1968-032-2 ID - 10_4153_CJM_1968_032_2 ER -
[1] 1. Ayoub, R., An introduction to the analytic theory of numbers (Providence, 1963). Google Scholar
[2] 2. Hardy, G. H. and Wright, E.M., An introduction to the theory of numbers (3rd éd.; Oxford, 1954). Google Scholar
[3] 3. Ingham, A. E., Some Tauberian theorems connected with the prime number theorem, J. London Math. Soc, 20 (1945), 171–180. Google Scholar
[4] 4. Landau, E., Handbuch der Lehre von der Verteilung der Primzahlen, I, II (Leipzig, 1909). Google Scholar
[5] 5. Widder, D. V., The Laplace transform (Princeton, 1946). Google Scholar
Cité par Sources :