Projects per year
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 
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics
Fingerprint
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