Limit Laws of Maximal Birkhoff Sums for Circle Rotations via Quantum Modular Forms

被引：0
|
作者：
Borda, Bence [1 ]
机构：
[1] Graz Univ Technol, Steyrergasse 30, A-8010 Graz, Austria
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 22期
基金：
奥地利科学基金会;
关键词：
THEOREMS;
D O I：
10.1093/imrn/rnad107
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Inthispaper, weshowhowquantummodularformsnaturallyariseintheergodictheoryofcirclerotations. WorkingwiththeclassicalBirkhoffsumS(N)(alpha) = Sigma(N)(n)= 1({n alpha}- 1/2), weprovethatthemaximumandtheminimumaswellascertainexponentialmomentsof S-N( r) asfunctionsof r.is an element of Q satisfyadirectanalogueofZagier'scontinuityconjecture, originallystatedforaquantuminvariantofthefigure-eightknot. Asacorollary, wefindthelimitdistributionof max 0 <= N<M-N(S)(alpha) and min0 <= N<M-N(S)(alpha) witharandoma alpha is an element of[0,1].
引用
收藏
页码：19340 / 19389
页数：50
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