We prove the existence of reciprocity formulae for sums of the form [Formula Presented] where f is a piecewise C1 function, featuring an alternating phenomenon not visible in the classical case where f(x) = x. We deduce bounds for these sums in terms of the continued fraction expansion of h/k.
Partial sums of the cotangent function
Bettin S.;Drappeau S.
2020
Abstract
We prove the existence of reciprocity formulae for sums of the form [Formula Presented] where f is a piecewise C1 function, featuring an alternating phenomenon not visible in the classical case where f(x) = x. We deduce bounds for these sums in terms of the continued fraction expansion of h/k.
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