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math.CA2017
Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the Möbius function. The estimate is remarkably sharp in comparison to…
math.CA2017
A criterion related to the Riemann Hypothesis
Helmut Maier, Michael Th. Rassias
A crucial role in the Nyman-Beurling-Báez-Duarte approach to the Riemann Hypothesis is played by the distance \[ d_N^2:=\inf_{A_N}\frac{1}{2π}\int_{-\infty}^\infty\left|1-ζA_N\left…
math.CA2017
From a cotangent sum to a generalized totient function
Michael Th. Rassias
In this paper we investigate a certain category of cotangent sums and more specifically the sum $$\sum_{m=1}^{b-1}\cot\left(\frac{πm}{b}\right)\sin^{3}\left(2πm\frac{a}{b}\right)\:…