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math.CA2024
Sharp Fourier decay estimates for measures supported on the well-approximable numbers
Robert Fraser, Thanh Nguyen
We construct a measure on the well-approximable numbers whose Fourier transform decays at a nearly optimal rate. This gives a logarithmic improvement on a previous construction of…
math.NT2024
Oscillatory integrals with phases arising from algebraic number fields
Robert Fraser
We develop a theory of oscillatory integrals whose phase is given by the trace of a polynomial over an algebraic number field. We present an application to the singular integral fo…