106 RANDOM NUMBERS 3.3.4 An upper bound for (Unable to start debugging on the web server)
106 RANDOM NUMBERS 3.3.4 An upper bound for the discrepancy can be found by using exponential sums. Let w = earijrn be a primitive mth root of unity. If (Q, . . . , zt) and (yl, . . . , yt) are two vectors with all components in the range 0 1. xj, yj < m, we have W(51-Y1)211+…+(Zt-Yt)Ut = mt, if (XI,. . . , xt) =(~1,. . . , yt); c 0, if(xl,…,xt) # (YI,… ,yt). O