Geodesic
On reciprocity formulas for Apostol's Dedekind sums and their analogues
Journal of integer sequences, Tome 17 (2014) no. 5.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Using the Euler-MacLaurin summation formula, we give alternative proofs for the reciprocity formulas of Apostol's Dedekind sums and generalized Hardy-Berndt sums $s_{3,p}(b,c)$ and $s_{4,p}(b,c)$. We also obtain an integral representation for each sum.
Classification : 11F20, 11B68, 65B15
Keywords: Dedekind sum, Hardy-Berndt sum, Bernoulli polynomial, Euler-Maclaurin formula 
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     author = {Da\u{g}l{\i}, M.Cihat and Can, M\"um\"un},
     title = {On reciprocity formulas for {Apostol's} {Dedekind} sums and their analogues},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {17},
     number = {5},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_5_a2/}
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Dağlı, M.Cihat; Can, Mümün. On reciprocity formulas for Apostol's Dedekind sums and their analogues. Journal of integer sequences, Tome 17 (2014) no. 5. http://geodesic.mathdoc.fr/item/JIS_2014__17_5_a2/