Samir Belhadj, Mouloud Goubi, "On the Vasyunin Cotangent sums related to Riemann Hypothesis," WSEAS Transactions on Mathematics, vol. 19, pp. 676-682, 2020, DOI:10.37394/23206.2020.19.74
Samir Belhadj, Mouloud Goubi. On the Vasyunin Cotangent sums related to Riemann Hypothesis.
WSEAS Transactions on Mathematics. 2020;19:676-682. 10.37394/23206.2020.19.74
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
On the Vasyunin Cotangent sums related to Riemann Hypothesis
Authors: ,
Abstract: In this work, we are interested by Vasyunin cotangent-sum V (p/q) encountered in computation of the inner product arising in the Baez-Duarte-Balazard criterion for Riemann hypothesis. By hint of generating functions theory and introduction of double Euclidean algorithm, we give series expansions of V (p/q) and the symmetric sum S (p, q) = V (p/q)+V (q/p) . These calculus permit to deduce another reformulation of Vasyunin formula. This study is a complement of the recent work of M. Goubi concerning special case V (1/q).
Pages: 676-682 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 19, 2020, Art. #74 DOI: 10.37394/23206.2020.19.74
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