Fourier Optimization and Quadratic Forms
Keyword(s):
Abstract We 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.
1946 ◽
Vol s1-21
(4)
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pp. 252-257
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Keyword(s):
1960 ◽
Vol 258
(1294)
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pp. 412-420
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1946 ◽
Vol s1-21
(4)
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pp. 257-264
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1984 ◽
Vol 96
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pp. 133-137
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2007 ◽
Vol 03
(04)
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pp. 541-556
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1955 ◽
Vol 7
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pp. 150-154
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