Abstract
If a and b are integers let
Let n be an integer, positive, negative or zero, and let r be a positive integer. Consider the sum
Usually, the sum is taken over all × such that 1 ≤ x ≤ r and (x, r) = 1, but it could be over any reduced residue system (mod r). This is because, if x ≡ x′ (mod r) then e(nx, r) = e(nx′, r). The sum c(n,r) is called a Ramanujan sum. For fixed r, and with n restricted to the positive integers, we obtain an arithmetical function c(·, r). Some authors devote this function by cr, so that cr(n) = c(n, r)
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© 1986 Springer-Verlag New York Inc.
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McCarthy, P.J. (1986). Ramanujan Sums. In: Introduction to Arithmetical Functions. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8620-9_2
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DOI: https://doi.org/10.1007/978-1-4613-8620-9_2
Publisher Name: Springer, New York, NY
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