= Hardy-Littlewood circle method
{c}
The circle method represents a weighted additive count as an integral of products of <exponential sums> against a character. Near rationals with small denominator, <major arcs> produce a structured main term involving a <singular series> and an archimedean singular integral. Away from those rationals, <minor arcs> require cancellation bounds. The partition and approximation estimates depend on the problem; a formal integral alone is not a positivity proof.
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