Formula:7579

Digital Library of Mathematical Functions ID 21.5.E7

${\displaystyle{\displaystyle\boldsymbol{{\Gamma}}=\begin{bmatrix}\mathbf{I}_{g}&\mathbf{B}\\ \boldsymbol{{0}}_{g}&\mathbf{I}_{g}\end{bmatrix}\Rightarrow\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}+\mathbf{B}\right)=\theta\left(\mathbf{z}+\tfrac{1}{2}\operatorname{diag}\mathbf{B}\middle|\boldsymbol{{\Omega}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$: Riemann theta function
• ${\displaystyle{\displaystyle g}}$: positive integer
• ${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$: a Riemann matrix
• ${\displaystyle{\displaystyle\operatorname{diag}\mathbf{A}}}$: Transpose of [ A 11 , A 22 , … , A ⁢ g g ]
• ${\displaystyle{\displaystyle\boldsymbol{{\Gamma}}}}$: 21.5.E1
 

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