Zeros

From DRMF
Jump to navigation Jump to search

Zeros

Distribution

Failed to parse (syntax error): {\displaystyle {\displaystyle Z(t) = \exp@{\iunit \vartheta(t)} \RiemannZeta@{\tfrac{1}{2}+\iunit t} }}

Substitution(s): Failed to parse (unknown function "\ph"): {\displaystyle {\displaystyle {\displaystyle \vartheta(t) \equiv \ph@@{\EulerGamma@{\tfrac{1}{4} + \tfrac{1}{2}\iunit t}} - \tfrac{1}{2} t \ln@@{\cpi}}}}


Constraint(s): Failed to parse (unknown function "\Real"): {\displaystyle {\displaystyle Z(t)\in\Real}} &
is chosen to make real &
Failed to parse (unknown function "\ph"): {\displaystyle {\displaystyle \ph@@{\EulerGamma@{\tfrac{1}{4}+\tfrac{1}{2}\iunit t}}}} assumes its principal value


Riemann-Siegel Formula

Failed to parse (syntax error): {\displaystyle {\displaystyle Z(t) = 2 \sum_{n=1}^m \frac{\cos@{\vartheta(t) - t \ln@@{n}}}{n^{1/2}} + R(t) }}

This formula has the name: Riemann-Siegel formula