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math.CA2019
On Bourgain's counterexample for the Schrödinger maximal function
Lillian B. Pierce
This paper provides a rigorous derivation of a counterexample of Bourgain, related to a well-known question of pointwise a.e. convergence for the solution of the linear Schrödinger…
math.NT2019
Burgess bounds for short character sums evaluated at forms
Lillian B. Pierce, Junyan Xu
In this work we establish a Burgess bound for short multiplicative character sums in arbitrary dimensions, in which the character is evaluated at a homogeneous form that belongs to…