Fourier optimization and quadratic forms
Peer reviewed, Journal article
Published version
Åpne
Permanent lenke
https://hdl.handle.net/11250/3023439Utgivelsesdato
2021Metadata
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- Institutt for matematiske fag [2530]
- Publikasjoner fra CRIStin - NTNU [38677]
Sammendrag
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 Cramér-type result on the maximum gap between primes represented by a given positive definite quadratic form.