Z ( t ) = exp ( i ϑ ( t ) ) \RiemannZeta @ 1 2 + i t 𝑍 𝑡 imaginary-unit italic-ϑ 𝑡 \RiemannZeta @ 1 2 imaginary-unit 𝑡 {\displaystyle{\displaystyle{\displaystyle Z(t)=\exp\left(\mathrm{i}\vartheta(% t)\right)\RiemannZeta@{\tfrac{1}{2}+\mathrm{i}t}}}} {\displaystyle Z(t) = \exp@{\iunit \vartheta(t)} \RiemannZeta@{\tfrac{1}{2}+\iunit t} }
Z ( t ) = 2 ∑ n = 1 m cos ( ϑ ( t ) - t ln n ) n 1 / 2 + R ( t ) 𝑍 𝑡 2 superscript subscript 𝑛 1 𝑚 italic-ϑ 𝑡 𝑡 𝑛 superscript 𝑛 1 2 𝑅 𝑡 {\displaystyle{\displaystyle{\displaystyle Z(t)=2\sum_{n=1}^{m}\frac{\cos\left% (\vartheta(t)-t\ln n\right)}{n^{1/2}}+R(t)}}} {\displaystyle Z(t) = 2 \sum_{n=1}^m \frac{\cos@{\vartheta(t) - t \ln@@{n}}}{n^{1/2}} + R(t) }