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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  Epub ahead of print  24 Feb 2022 
ASJC Scopus subject areas
 Mathematics(all)
 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