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Proceedings of the American Mathematical Society

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On a question of Rademacher concerning Dedekind sums


Author: Laurence Pinzur
Journal: Proc. Amer. Math. Soc. 61 (1976), 11-15
MSC: Primary 10A20
DOI: https://doi.org/10.1090/S0002-9939-1976-0429717-6
MathSciNet review: 0429717
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Abstract: Rademacher raised the following question concerning the ordinary Dedekind sum $ s(h,k)$. If $ {h_1}/{k_1}$ and $ {h_2}/{k_2}$ are adjacent Farey fractions such that $ s({h_1},{k_1}) > 0$ and $ s\left( {{h_2},{k_2}} \right) > 0$, is it necessarily true that $ s({h_1} + {h_2},{k_1} + {k_2}) \geqslant 0$? The answer to this question is found to be no. In fact, a characterization of all pairs of adjacent Farey fractions where the answer to Rademacher's question is no is given.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0429717-6
Article copyright: © Copyright 1976 American Mathematical Society