Dedekind Sums and Some Generalized Fibonacci and Lucas Sequences

Dilcher, Karl; Meyer, Jeffrey L.

doi:10.1080/00150517.2010.12428105

The Fibonacci Quarterly

2010

DOI: 10.1080/00150517.2010.12428105

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Dedekind Sums and Some Generalized Fibonacci and Lucas Sequences

Karl Dilcher,

Jeffrey L. Meyer

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2024

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Distribution of values of Hardy sums over Chebyshev polynomials

Wang,

Xu,

Jia

2024

MATH

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<abstract><p>This paper mainly studied the distribution of values of Hardy sums involving Chebyshev polynomials. By using the method of analysis and the arithmetic properties of Hardy sums and Chebyshev polynomials of the first kind, we obtained a sharp asymptotic formula for the hybrid mean value of Hardy sums $ S_5(h, q) $ involving Chebyshev polynomials of the first kind. In addition, we also gave the value of Hardy sums $ S(h, q) $ and $ S_{3}(h, q) $ involving Chebyshev polynomials. Finally, we found the reciprocal formulas of $ S_{3}(h, q) $ and $ S_{4}(h, q) $ involving Chebyshev polynomials of the first kind.</p></abstract>

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Distribution of values of Hardy sums over Chebyshev polynomials

Wang,

Xu,

Jia

2024

MATH

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Dedekind Sums and Some Generalized Fibonacci and Lucas Sequences

Cited by 1 publication

References 7 publications

Distribution of values of Hardy sums over Chebyshev polynomials

Distribution of values of Hardy sums over Chebyshev polynomials

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