Article
Cyclotomic Expressions for Representation Functions
Authors
Abstract
Given a subset A of the natural numbers N = {0, 1, 2, · · · } (resp. of the ring Z/NZ of residue classes modulo a positive integer N), we introduce certain sums of roots of unity associated with A. We study some of their proper- ties, and we use them to obtain new expressions for the classical functions that characterize A, i.e. of the representation function, the counting function and the characteristic function of A. We also give an example of computations of the representation function using such expressions.
Keywords
Representation function, exponential sums, cyclotomic fields.
Citation
Helou, C. (2019). Cyclotomic expressions for representation functions. Uniform Distribution Theory, 14(1), 123–140. https://doi.org/10.2478/udt-2019-0008
C. Helou, “Cyclotomic expressions for representation functions,” Uniform Distribution Theory, vol. 14, no. 1, pp. 123–140, 2019, doi: 10.2478/udt-2019-0008.
Helou C. Cyclotomic expressions for representation functions. Uniform Distribution Theory. 2019;14(1):123–140. doi:10.2478/udt-2019-0008.
Helou, C. (2019), ‘Cyclotomic expressions for representation functions’, Uniform Distribution Theory, 14(1), pp. 123–140. Available at: https://doi.org/10.2478/udt-2019-0008.
Helou, Charles. “Cyclotomic Expressions for Representation Functions.” Uniform Distribution Theory, vol. 14, no. 1, 2019, pp. 123–140. https://doi.org/10.2478/udt-2019-0008.
Helou, Charles. “Cyclotomic Expressions for Representation Functions.” Uniform Distribution Theory 14, no. 1 (2019): 123–140. https://doi.org/10.2478/udt-2019-0008.
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Published by: Engineering Journals
