One problem of D. S. Mitrinovič and its generalization
Nikola Rosić (2001)
Kragujevac Journal of Mathematics
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Nikola Rosić (2001)
Kragujevac Journal of Mathematics
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Emmanuel Tsukerman (2015)
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Using a generalization due to Lerch [Bull. Int. Acad. François Joseph 3 (1896)] of a classical lemma of Zolotarev, employed in Zolotarev's proof of the law of quadratic reciprocity, we determine necessary and sufficient conditions for the difference of two Dedekind sums to be in 8ℤ. These yield new necessary conditions for equality of two Dedekind sums. In addition, we resolve a conjecture of Girstmair [arXiv:1501.00655].
Yumiko Nagasaka, Kaori Ota, Chizuru Sekine (2003)
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Studia Mathematica
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The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated....