Irregularities of Distribution, Ii
نویسنده
چکیده
(1.2) \D[zu ..., zn ; B(x, r)]\ > c2(K, e). n < Note that the exponent {\ — (1/2K) e) of n is essentially the best possible: (2 — (1/2K) e) cannot be replaced by the exponent (2 — (1/2K) + e) with e > 0. Note further that (1.1) or (1.2) above guarantees the existence of a ball in U with 'error' very large as compared to that of boxes in U with sides parallel to the axes. We recall that in 1954 Roth [7] proved the existence of a box A contained in U with sides parallel to the axes and with 'error'
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