Geodesic
Limit theorem for trigonometric sums. Theory of curlicues
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 6, pp. 1023-1029

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This paper is a discussion of the behaviour of the trigonometric sums $\sum\exp\{2\pi\alpha n^2\}$ and their limiting distribution as a function of $N$. The analysis is based upon another application of the renormalization group theory. 
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     author = {Ya. G. Sinai},
     title = {Limit theorem for trigonometric sums. {Theory} of curlicues},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     volume = {63},
     number = {6},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/RM_2008_63_6_a3/}
}
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Ya. G. Sinai. Limit theorem for trigonometric sums. Theory of curlicues. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 63 (2008) no. 6, pp. 1023-1029. http://geodesic.mathdoc.fr/item/RM_2008_63_6_a3/