A Reciprocity Formula for a Cotangent Sum

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Period functions and cotangent sums (2011, methodology): “In [Bettin and Conrey 2011] we showed that c0(h/k) satisfies the reciprocity formula c0 (h k ) + k h c0 ( k h ) − 1 πh = i 2 ψ0 (h k ) (14) (and in particular that c0(h/k) can be computed to within a prescribed accuracy in a time that is polynomial in log k).”