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Central limit theorems in the geometry of numbers

Michael Björklund (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori) ; Alexander Gorodnik
Electronic Research Announcements in Mathematical Sciences (19359179). Vol. 24 (2017), p. 110-122.
[Artikel, refereegranskad vetenskaplig]

We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a Central Limit Theorem. Furthermore, we show that the Central Limit Theorem holds for the number of rational approximants for weighted Diophantine approximation in ?d. Our arguments exploit chaotic properties of the Cartan flow on the space of lattices.

Nyckelord: Central Limit Theorems; Diophantine approximation

Denna post skapades 2017-12-08.
CPL Pubid: 253653


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Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)



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