Abstract
AbstractWe prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer $\ell\ge 1$, we improve the error term in the partial sums of the number of representations of integers that are a multiple of $\ell$. This allows us to obtain unconditional Brun–Titchmarsh-type results in short intervals and a conditional Cramér-type result on the maximum gap between primes represented by a given positive definite quadratic form.
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