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• W2020177428 abstract "We show that the $n$-point correlation function for the fractional parts of a random linear form in $m$ variables has a limit distribution with power-like tail. The existence of the limit distribution follows from the mixing property of flows on ${rm SL}(m+1,{Bbb R})/{rm SL}(m+1,{Bbb Z})$. Moreover, we prove similar limit theorems (i) for the probability to find the fractional part of a random linear form close to zero and (ii) also for related trigonometric sums. For large $m$, all of the above limit distributions approach the classical distributions for independent uniformly distributed random variables." @default.
• W2020177428 created "2016-06-24" @default.
• W2020177428 creator A5014853361 @default.
• W2020177428 date "2000-08-01" @default.
• W2020177428 modified "2023-09-30" @default.
• W2020177428 title "The $bm{n}$-point correlations between values of a linear form" @default.
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• W2020177428 doi "https://doi.org/10.1017/s0143385700000626" @default.
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