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Some Finite Analogues of the Poisson Summation Formula†

Published online by Cambridge University Press:  20 January 2009

L. Carlitz
L. Carlitz
Affiliation:
Duke University, U.S.A.
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1. Guinand (2) has obtained finite identities of the type

where m, n, N are positive integers and either

or

where γ is Euler's constant and the notation ∑′ indicates that when x is integral the term r = x is multiplied by ½. Clearly there is no loss of generality in taking N = 1 in (1.1).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , Issue 3 , June 1961 , pp. 133 - 138
Copyright
Copyright © Edinburgh Mathematical Society 1961

References

REFERENCES

(1)Carlitz, L., Some generalized multiplication formulas for Bernoulli polynomials and related functions, Monatshefte fur Mathematik, 65 (to appear).Google Scholar
(2)Guinand, A. P., Some finite identities connected with Poisson's summation formula, Proceedings of the Edinburgh Mathematical Society, 12 (1960), 17–25.CrossRefGoogle Scholar
(3)Mordell, L. J., Integral formulas of arithmetic character, Journal of the London Mathematical Society, 33 (1957), 371–375.Google Scholar