Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$

Authors : Yamilet Quintana, Héctor Torres-guzmán

Pages : 188-201

Doi:10.32323/ujma.602178

View : 25 | Download : 11

Publication Date : 2019-12-26

Article Type : Research

Abstract :The main purpose of this paper is to show some relations between the Riemann zeta function and the generalized Bernoulli polynomials of level $m$. Our approach is based on the use of Fourier expansions for the periodic generalized Bernoulli functions of level $m$, as well as  quadrature formulae of Euler-Maclaurin type. Some illustrative examples involving such relations are also given.
Keywords : Bernoulli polynomials, Euler-Maclaurin quadrature formulae, generalized Bernoulli polynomials of level $m$, quadrature formula, Riemann zeta function