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math.DS2021
A Remarkable Summation Formula, Lattice Tilings, and Fluctuations
J. J. P. Veerman, L. S. Fox, P. J. Oberly
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any re…
math.DS2020
Statistics of a Family of Piecewise Linear Maps
J. J. P. Veerman, P. J. Oberly, L. S. Fox
We study statistical properties of the truncated flat spot map . In particular, we investigate whether for large , the deviations $\sum_{i=0}^{n-1} \left(f_t^i(x_0)-\fra…