In this paper, we study the functional equation, f (x+y)f (x)f (y) = d sin x sin y. Some generalizations of the above functional equation are also considered.
We consider a cotangent sum related to Estermann's Zeta function. We provide an elementary and self-contained improvement of the error term in an asymptotic formula proved by V. I. Vasyunin.
In this paper, by the application of methods of weight functions and the use of analytic techniques, a multidimensional more accurate half-discrete Hilbert-type inequality with the kernel of the hyperbolic cotangent function is proved. We show that the constant factor related to the Riemann zeta function is the best possible. Equivalent forms as well as… (More)