Geodesic
On reciprocity formulas for Apostol's Dedekind sums and their analogues
Journal of integer sequences, Tome 17 (2014) no. 5
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 
@article{JIS_2014__17_5_a2,
     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},
     year = {2014},
     volume = {17},
     number = {5},
     zbl = {1286.11056},
     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/