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Abstract
Abstract: Given a variety with coefficients in , we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise this to more general Weil divisors, where we obtain a geometric interpretation of the covariance matrix. For our results we develop a version of the Erdős–Kac theorem that applies to fairly general integer sequences and does not require a positive exponent of level of distribution.
Original language  English 

Pages (fromto)  30893128 
Number of pages  40 
Journal  Transactions of the American Mathematical Society 
Volume  375 
Issue number  5 
Early online date  24 Feb 2022 
DOIs  
Publication status  Published  31 Dec 2022 
Bibliographical note
Funding Information:Received by the editors September 6, 2020, and, in revised form, May 27, 2021. 2020 Mathematics Subject Classification. Primary 14G05; Secondary 60F05, 11N36. The first author was supported by the Austrian Science Fund (FWF), projects F5512 and Y901. The second author was supported by EPSRC grant EP/R021422/2.
ASJC Scopus subject areas
 General Mathematics
 Applied Mathematics
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Dive into the research topics of 'Multivariate normal distribution for integral points on varieties'. Together they form a unique fingerprint.Projects
 1 Finished

Quantitative arithmetic geometry
Engineering and Physical Sciences Research Council
1/04/19 → 30/09/21
Project: Research council