ON A FORMULA FOR THE REGULARIZED DETERMINANT OF ZETA FUNCTIONS WITH APPLICATION TO SOME DIRICHLET SERIES
Mounir Hajli
Abstract
Abstract In this paper, we study a large class of zeta functions. We evaluate explicitly the special values of these zeta functions and the associated derivatives at $0$. As an application, we recover several results on the zeta functions defined by two polynomials already obtained in the literature.
Topics & Concepts
Dirichlet seriesRiemann zeta functionPrime zeta functionArithmetic zeta functionMathematicsSeries (stratigraphy)Class (philosophy)Dirichlet distributionZeta function regularizationPolylogarithmPure mathematicsApplied mathematicsMathematical analysisAlgebra over a fieldComputer scienceArtificial intelligenceBoundary value problemBiologyPaleontologyAdvanced Mathematical IdentitiesAnalytic Number Theory ResearchMathematical functions and polynomials