SiegelTheta

SiegelTheta[Ω,s]

gives the Siegel theta function with Riemann modular matrix Ω and vector s.

SiegelTheta[{ν1,ν2},Ω,s]

gives the Siegel theta function with characteristics ν1 and ν2.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The matrix Ω must be symmetric, with positive definite imaginary part.
  • If Ω is a p×p matrix, the vectors s and v or νi must have length p.
  • , where n ranges over all possible vectors in the p-dimensional integer lattice.
  • , where n ranges over all possible vectors in the p-dimensional integer lattice.
  • SiegelTheta can be evaluated to arbitrary numerical precision.

Examples

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Basic Examples  (2)

Evaluate numerically:

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Scope  (4)

Generalizations & Extensions  (2)

Applications  (2)

Properties & Relations  (2)

Possible Issues  (2)

Neat Examples  (1)

See Also

EllipticTheta

Introduced in 2007
(6.0)