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Article Dans Une Revue Array Année : 2017

Explicit and asymptotic formulae for Vasyunin-cotangent sums

Résumé

For coprime numbers p and q, we consider the Vasyunin-cotangent sum V(q, p)= ?p?1 k=1 {kq/p} cot (?k/p). First, we prove explicit formula for the symmetric sum V(p,q)+ V(q,p) which is a new reciprocity law for the sums above. This formula can be seen as a complement to the Bettin-Conrey result [13, Theorem 1]. Second, we establish an asymptotic formula for V(p,q). Finally, by use of continued fraction theory, we give a formula for V(p,q) in terms of continued fraction of p/q.
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Dates et versions

hal-04463441 , version 1 (17-02-2024)

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Mouloud Goubi, Abdelmejid Bayad, Mohand Hernane. Explicit and asymptotic formulae for Vasyunin-cotangent sums. Array, 2017, 102 (116), pp.155-174. ⟨10.2298/PIM1716155G⟩. ⟨hal-04463441⟩
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