Article
Kloosterman Sums for Modified Van Der Corput Sequences
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Abstract
For every integer n ∈ N, let R(n) be the integer obtained by reversing the order of the base-g digits of n and call R(n) the reversal of n (with respect to g). In this paper, we introduce and study a sequence C(g) = {R(n)}∞ n=1 which is closely related to the van der Corput sequence. We establish a few fundamental divisibility properties of reversals that lead to sharp estimates for the number of solutions to a system of congruences of the form n ≡ s (mod v) and R(n) ≡ t (mod w) (s, v, t, w ∈ N).
Keywords
van der Corput sequences, integer sequences, congruences, exponential sums.
Citation
Banks, W., Saidak, F., & Sakata, M. (2007). Kloosterman sums for modified van der corput sequences. Uniform Distribution Theory, 2(1), 39–52.
W. Banks, F. Saidak and M. Sakata, “Kloosterman sums for modified van der corput sequences,” Uniform Distribution Theory, vol. 2, no. 1, pp. 39–52, 2007.
Banks W, Saidak F, Sakata M. Kloosterman sums for modified van der corput sequences. Uniform Distribution Theory. 2007;2(1):39–52.
Banks, W., Saidak, F. and Sakata, M. (2007), ‘Kloosterman sums for modified van der corput sequences’, Uniform Distribution Theory, 2(1), pp. 39–52.
Banks, William, et al. “Kloosterman Sums for Modified Van Der Corput Sequences.” Uniform Distribution Theory, vol. 2, no. 1, 2007, pp. 39–52.
Banks, William, Filip Saidak, and Mayumi Sakata. “Kloosterman Sums for Modified Van Der Corput Sequences.” Uniform Distribution Theory 2, no. 1 (2007): 39–52.
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Published by: Engineering Journals
