DLMF:21.6.E6 (Q6894): Difference between revisions

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		Property / Symbols used
			Q11961
		Property / Symbols used: Q11961 / rank
			Normal rank
		Property / Symbols used: Q11961 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}$ \boldsymbol{{\alpha}}
		Property / Symbols used: Q11961 / qualifier
			xml-id: C21.S1.XMD4.m1dec
		Property / Symbols used
			Q11962
		Property / Symbols used: Q11962 / rank
			Normal rank
		Property / Symbols used: Q11962 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{{\beta}}}}$ \boldsymbol{{\beta}}
		Property / Symbols used: Q11962 / qualifier
			xml-id: C21.S1.XMD5.m1dec

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Latest revision as of 14:51, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:21.6.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\theta\left(\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)=\frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}{\mathbb{Z}^{g}}/{\mathbb{Z}^{g}}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}{\mathbb{Z}^{g}}/{\mathbb{Z}^{g}}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\theta\left(\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right),}}$

0 references

DLMF id

DLMF:21.6.E6

0 references

Symbols used

Riemann theta function

Defining formula

${\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$

xml-id

C21.S2.E1.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2abdec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2abdec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2abdec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2abdec

0 references

Q10818

Defining formula

${\displaystyle{\displaystyle\mathbb{Z}}}$

xml-id

introduction.Sx4.p2.t1.r20.m2abdec

0 references

Q11959

Defining formula

${\displaystyle{\displaystyle g}}$

xml-id

C21.S1.XMD1.m1cdec

0 references

Q11960

Defining formula

${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$

xml-id

C21.S1.XMD3.m1bdec

0 references

Q11961

Defining formula

${\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}$

xml-id

C21.S1.XMD4.m1dec

0 references

Q11962

Defining formula

${\displaystyle{\displaystyle\boldsymbol{{\beta}}}}$

xml-id

C21.S1.XMD5.m1dec

0 references

 

Sitelinks

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