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Showing 1 to 4 of 4 for “"arithmetic statistics"”.
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Arithmetic statistics of algebraic groups
This thesis investigates various problems in the arithmetic statistics of algebraic groups, focusing on the distribution and properties of algebraic groups of number-theoretic interest. New results obtained throughout this thesis are unified by the development and application of methods, primarily …
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Arithmetic statistics and Vinberg representations
In this thesis, we obtain results in arithmetic statistics through Vinberg representations. Very often, the rational and integral orbits of Vinberg representations encode information about certain arithmetic objects of interest. In view of that, we can use Bhargava's techniques in …
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
… and partially proven a strong link between the arithmetic of these curves and the rational orbits of these representations. In this thesis, we complete Thorne's picture and show that $2$-Selmer elements of the Jacobians of the smooth curves in each family can be parametrised by integral orbits …
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Counting elliptic curves of bounded Faltings height
… difficult to understand directly, the study of arithmetic statistics instead looks at what happens "on average", using heights to make this notion rigorous. Previous work has primarily used the naive height, which can be calculated easily but is not defined intrinsically. We give an asymptotic …