Article
An Application of Ramanujan Sums to Equirepartition Modulo an Odd Integer
Authors
Abstract
Following a result of Myerson on finite fields, we prove that for an odd number n3, the 2φ(n)/2 sums: ±1 ± 2 · · · ± i · · · ± (n − 1)/2 , where the terms i are all the invertibles modulo n from 1 to (n − 1)/2 , are distributed among the classes modulo n as uniformly as possible. We also determine and prove that the distribution of the 2(n−1)/2 sums: ±1 ± 2 · · · ± (n − 1)/2 , where all the elements from 1 to (n − 1)/2 are represented once, is also asymp- totically equidistributed.
Keywords
Ramanujan sum, Euler totient, Jacobi symbol, primitive root of unity.
Citation
Balandraud, E. (2007). An application of ramanujan sums to equirepartition modulo an odd integer. Uniform Distribution Theory, 2(2), 1–17.
E. Balandraud, “An application of ramanujan sums to equirepartition modulo an odd integer,” Uniform Distribution Theory, vol. 2, no. 2, pp. 1–17, 2007.
Balandraud E. An application of ramanujan sums to equirepartition modulo an odd integer. Uniform Distribution Theory. 2007;2(2):1–17.
Balandraud, E. (2007), ‘An application of ramanujan sums to equirepartition modulo an odd integer’, Uniform Distribution Theory, 2(2), pp. 1–17.
Balandraud, Eric. “An Application of Ramanujan Sums to Equirepartition Modulo an Odd Integer.” Uniform Distribution Theory, vol. 2, no. 2, 2007, pp. 1–17.
Balandraud, Eric. “An Application of Ramanujan Sums to Equirepartition Modulo an Odd Integer.” Uniform Distribution Theory 2, no. 2 (2007): 1–17.
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Published by: Engineering Journals
