A function field version of the circle method is applied to a cubic hypersurface X defined over a finite field Fq. Using the correspondence between Fqrational curves and Fq(t)points, we deduce the dimension and irreducibility of the moduli space of rational curves on X passing through two fixed points. Furthermore, we study Manin’s conjecture over function fields and obtain an example where the conjecture holds after removing a thin set of points. This leads to an application which can be seen as the prime number theorem for 0cycles on P2.
Date of Award  1 Oct 2019 

Original language  English 

Awarding Institution   The University of Bristol


Supervisor  Andrew R Booker (Supervisor) & Tim Browning (Supervisor) 

 number theory
 function fields
 rational points
 rational curves
 Manin's conjecture
 Peyre's constant
 0cycles
Rational points in function fields
Manzateanu, A. (Author). 1 Oct 2019
Student thesis: Doctoral Thesis › Doctor of Philosophy (PhD)