We prove several results about integers represented by positive definite
quadratic forms, using a Fourier analysis approach. In particular, for an
integer ℓ≥1, we improve the error term in the partial sums of the
number of representations of integers that are a multiple of ℓ. This
allows us to obtain unconditional Brun-Titchmarsh-type results in short
intervals, and a conditional Cram\'er-type result on the maximum gap between
primes represented by a given positive definite quadratic form.Comment: 31 pages. Minor edits. To appear in Q. J. Mat