On a question of Rademacher concerning Dedekind sums
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- by Laurence Pinzur PDF
- Proc. Amer. Math. Soc. 61 (1976), 11-15 Request permission
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.References
- Dean Hickerson, Continued fractions and density results for Dedekind sums, J. Reine Angew. Math. 290 (1977), 113–116. MR 439725, DOI 10.1515/crll.1977.290.113
- Ivan Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1972. MR 0344181 H. Rademacher, Proc. 1963 Number Theory Conf., Univ. of Colorado, Boulder, Colo., 1963.
- Hans Rademacher and Emil Grosswald, Dedekind sums, The Carus Mathematical Monographs, No. 16, Mathematical Association of America, Washington, D.C., 1972. MR 0357299
Additional Information
- © Copyright 1976 American Mathematical Society
- 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