Effective Equidistribution in Homogeneous Dynamics with Applications in Number Theory

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" Effective Equidistribution in Homogeneous Dynamics with Applications in Number Theory "
McAdam, Taylor Jane Mohammadi, Amir

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	904761
Doc. No	:	TL28k763gr
Main Entry	:	McAdam, Taylor Jane
Title & Author	:	Effective Equidistribution in Homogeneous Dynamics with Applications in Number Theory\ McAdam, Taylor JaneMohammadi, Amir
College	:	UC San Diego
Date	:	2019
student score	:	2019
Abstract	:	We study the asymptotic distribution of almost-prime entries in horospherical flows on the quotient of SL(n,R) by a lattice, where the lattice is either cocompact or SL(n,Z). In the cocompact case, we obtain a result that implies density for almost-primes in horospherical flows where the number of prime factors is independent of the basepoint, and in the space of lattices we show the density of almost-primes in abelian horospherical orbits of points satisfying a certain Diophantine condition. Along the way we give an effective equidistribution result for arbitrary horospherical flows on the space of lattices, as well as an effective rate for the equidistribution of arithmetic progressions in abelian horospherical flows.
Added Entry	:	Mohammadi, Amir
Added Entry	:	UC San Diego