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Poisson's Summation Formula in several Variables and some Applications to the Theory of Numbers

Published online by Cambridge University Press:  24 October 2008

L. J. Mordell
L. J. Mordell
Affiliation:
formerly of St John's College
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Extract

In a recent paper, Poisson's summation formula

was proved very simply by integration by parts, subject to the conditions:

(α) for all real values of x, f(x) and f′(x) are continuous and f (x)→0, f′ (x)→0 as |x| → ∞.

(β) f(x) and f″(x) are such that the integrals, converge.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 4 , October 1929 , pp. 412 - 420
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

* “Poisson's Summation Formula and the Riemann Zeta Function,” Journal of the London Mathematical Society, 4 (1929).Google Scholar

* Cf. Landau, , “Die Bedeutungslosigkeit der Pfeiffer'schen Methode für die analytische Zahlentheorie,” Monatshefte für Mathematik und Physik, 34 (1926), 1–36, especially 1–9;CrossRefGoogle ScholarVorlesungen über Zahlentheorie, 2 (1927), 204–206Google Scholar

* “Neuer Beweis des Satzes von Minkowski über lineare Formen,” Mathematische Annalen, 87 (1922), 36–38.CrossRefGoogle Scholar

* The convention to be adopted for the corners of the parallelogram (3·2) is not as suggested.Google Scholar