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SiegelTheta

SiegelTheta
gives the Siegel theta function with Riemann modular matrix and vector s.
SiegelTheta
gives the Siegel theta function with characteristics and .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The matrix must be symmetric, with positive definite imaginary part.
  • If is a matrix, the vectors s and v or 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.
Evaluate numerically:
Evaluate numerically:
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Evaluate SiegelTheta for higher-dimensional arguments:
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
SiegelTheta with characteristics and :
SiegelTheta with characteristics simplifies symbolically for special arguments:
Plot of the absolute value of SiegelTheta in the complex plane:
Define an Abelian function:
Plot of the real part:
In one dimension, SiegelTheta coincides with the EllipticTheta functions:
SiegelTheta satisfies the equations:
SiegelTheta requires a symmetric matrix:
The symmetric part:
Machine precision may be insufficient to obtain a correct answer:
Use arbitrary precision to check the result:
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