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ON DEDEKIND SUMS II REMARKS ON HIGHER DIMENSIONAL DEDEKIND SUMS
ON DEDEKIND SUMS II REMARKS ON HIGHER DIMENSIONAL DEDEKIND SUMSopenaire
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The American Mathematical Monthly, 2010
(2010). Farey Sums and Dedekind Sums. The American Mathematical Monthly: Vol. 117, No. 1, pp. 72-78.
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(2010). Farey Sums and Dedekind Sums. The American Mathematical Monthly: Vol. 117, No. 1, pp. 72-78.
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Bulletin of the London Mathematical Society, 2004
Let \(x= h/k\) for integers \(h\) and \(k,k> 0\). The classical Dedekind sum \(s(x)= s(h, k)\) is well defined as a function \(s: \mathbb{Q}\to\mathbb{Q}\). The authors prove that for every rational \(\alpha\neq 1/12\) there are infinitely many \(x\) such that \(s(x)= \alpha x\).
Myerson, G., Philips, N.
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Let \(x= h/k\) for integers \(h\) and \(k,k> 0\). The classical Dedekind sum \(s(x)= s(h, k)\) is well defined as a function \(s: \mathbb{Q}\to\mathbb{Q}\). The authors prove that for every rational \(\alpha\neq 1/12\) there are infinitely many \(x\) such that \(s(x)= \alpha x\).
Myerson, G., Philips, N.
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Dedekind zeta-functions and Dedekind sums
Science in China Series A: Mathematics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, Hongwen +2 more
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Czechoslovak Mathematical Journal
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Nianliang +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Nianliang +2 more
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DEDEKIND SUMS WITH SMALL DENOMINATORS
International Journal of Number Theory, 2012Let (m, n) = 1 and S(m/n) = 12s(m/n), where s(m/n) is the usual Dedekind sum. Then [Formula: see text]. Let q ≥ 1 be a divisor of n. We give a necessary and sufficient condition for [Formula: see text] and, thereby, generalize a result of Rademacher that concerns the case q = 1.
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2008
In this paper, we introduce Dedekind sums associated to lattices defined over finite fields. We establish the reciprocity law for them.
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In this paper, we introduce Dedekind sums associated to lattices defined over finite fields. We establish the reciprocity law for them.
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2016
Dedekind sums arose out of the study of elliptic functions and modular forms. They were iniially discovered by Dedekind but have since been studied for their many arithmetic properties. Much work has been done on Dedekind sums and in 1972 Rademacher and Grosswald released a book that summarised much of what was known, as well as providing a history of ...
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Dedekind sums arose out of the study of elliptic functions and modular forms. They were iniially discovered by Dedekind but have since been studied for their many arithmetic properties. Much work has been done on Dedekind sums and in 1972 Rademacher and Grosswald released a book that summarised much of what was known, as well as providing a history of ...
openaire +1 more source