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math.NT2020
On some Féjer-type trigonometric sums
R. B. Paris
We examine the four Féjer-type trigonometric sums of the form \[S_n(x)=\sum_{k=1}^n \frac{f(g(kx))}{k}\qquad (0<x<π)\] where , are chosen to be either or $\co…
math.NT2012★ 2 cited
Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function for positive integers
Michael A. Idowu
A new definition for the Dirichlet beta function for positive integer arguments is discovered and presented for the first time. This redefinition of the Dirichlet beta function, ba…
math.NT2012★ 2 cited
Elegant expressions and generic formulas for the Riemann zeta function for integer arguments
Michael A. Idowu
A new definition for the Riemann zeta function for all positive integer number s > 1 is presented. We discover a most elegant expression and easy method for calculating the Riemann…