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- W2318884218 abstract "The existence of certain formulae analogous to Poisson's summation formula ( 9 , pp. 60-64), where αβ = 2π, α > 0, and F c (x) is the Fourier cosine transform of f (x), but involving number-theoretic functions as coefficients, was first demonstrated by Voronoï ( 10 ) in 1904. He proved that where r(n) is an arithmetic function,/(x) is continuous in (a, b) and a(x) and i?(x) are analytic functions dependent on τ(n). Later, numerous papers were published by various authors giving formulae of this type involving d(n), the number of divisors of n ( 3 ), and r p (n), the number of ways of expressing n as the sum of p squares of integers ( 8 ). In 1937, Ferrar ( 4 ) developed a general theory of summation formulae, using complex analysis. Around that time, Guinand ( 5 ) also published papers where he developed the general theory from a different point of view. He applied the theory of mean convergence for the transforms of class L 2 ( 0 , ∞ ). Later in 1950, Bochner ( 1 ) gave a general summation formula." @default.
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- W2318884218 date "1969-01-01" @default.
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- W2318884218 title "A Summation Formula Involving σk(n), k > 1" @default.
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- W2318884218 doi "https://doi.org/10.4153/cjm-1969-104-3" @default.
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