Identities on poly-Dedekind sums
Advances in Difference Equations, 2020 Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums.
Lee-Chae Jang +2 more
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Generalized Dedekind Eta-Functions and Generalized Dedekind Sums [PDF]
Transactions of the American Mathematical Society, 1973 A transformation formula under modular substitutions is derived for a very large class of generalized Eisenstein series. The result also gives a transformation formula for generalized Dedekind eta-functions. Various types of Dedekind sums arise, and reciprocity laws are established.
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Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions
Advances in Difference Equations, 2021 The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group.
Yuankui Ma +4 more
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. [PDF]
Math Ann, 2023 Minelli P, Sourmelidis A, Technau M.
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On the infinite Borwein product raised to a positive real power. [PDF]
Ramanujan J, 2023 Schlosser MJ, Zhou NH.
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From partitions to Hodge numbers of Hilbert schemes of surfaces. [PDF]
Philos Trans A Math Phys Eng Sci, 2020 Gillman N +4 more
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Dedekind's eta-function and the cohomology of infinite dimensional Lie algebras. [PDF]
Proc Natl Acad Sci U S A, 1975 Garland H.
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A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with <i>p</i>-Modular Lattice Constructions. [PDF]
Entropy (Basel)Khodaiemehr H +5 more
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Mock Modularity at Work, or Black Holes in a Forest. [PDF]
Entropy (Basel)Alexandrov S.
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