Integral formulas for a Dirichlet series
Guy Laville (LMNO)
TL;DR
This paper derives an integral representation formula for a specific Dirichlet series with coefficients given by the Liouville function, providing new analytical tools for studying such series.
Contribution
It introduces a novel integral formula for Dirichlet series with Liouville function coefficients, expanding the analytical methods available for these series.
Findings
Provides an explicit integral representation for the Dirichlet series
Enables new approaches to analyze properties of the Liouville function
Offers potential applications in number theory and analytic continuation
Abstract
We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · advanced mathematical theories · Meromorphic and Entire Functions