Zeros

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Zeros

Distribution

Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Expected "(", "-", "[", "\\", "\\begin", "\\begin{", "\\{", "]", "^", "_", "{", "}", [ \t\n\r], [%$], [().], [,:;?!'], [/|], [0-9], [><~], [\-+*=], or [a-zA-Z] but "@" found.in 2:14"): {\displaystyle {\displaystyle Z(t) = \exp@{\iunit \vartheta(t)} \RiemannZeta@{\tfrac{1}{2}+\iunit t} }}

Substitution(s): Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \phin 1:67"): {\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 (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \Realin 1:38"): {\displaystyle {\displaystyle Z(t)\in\Real}} &
is chosen to make real &
Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \phin 1:31"): {\displaystyle {\displaystyle \ph@@{\EulerGamma@{\tfrac{1}{4}+\tfrac{1}{2}\iunit t}}}} assumes its principal value


Riemann-Siegel Formula

Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Expected "(", "-", "[", "\\", "\\begin", "\\begin{", "\\{", "]", "^", "_", "{", "}", [ \t\n\r], [%$], [().], [,:;?!'], [/|], [0-9], [><~], [\-+*=], or [a-zA-Z] but "@" found.in 3:30"): {\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