Geodesic
Series Expansion of a Cotangent Sum Related to the Estermann Zeta Function
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 343

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In this paper, we study the cotangent sum $c_0(\frac{q}{p})$ related to the Estermann zeta function for the special case when the numerator is equal to 1 and get two useful series expansions of $c_0(\frac{1}{p})$.
Classification : 11F20, 11E45 11M26
Keywords: Estermann zeta function, Vasyunin cotangent sum, generating function 
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     author = {Mouloud Goubi},
     title = {Series {Expansion} of a {Cotangent} {Sum} {Related} to the {Estermann} {Zeta} {Function}},
     journal = {Kragujevac Journal of Mathematics},
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     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a1/}
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Mouloud Goubi. Series Expansion of a Cotangent Sum Related to the Estermann Zeta Function. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 343 . http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a1/