acb_theta_jet_notransform

Before calling acb_theta_ql_jet, the function uses these formulas:

• if ord is zero and all and sqr are nonzero, the duplication formula \theta_{a,b}(z,\tau)^2 = \sum_{a'} (-1)^{a'^T b} \theta_{a',0}(0,2\tau) \theta_{a+a',0}(2z,2\tau), which needs only the 2^g functions \theta_{a,0} at 2\tau;
• if all is zero and ab is zero, \theta_{0,0}(z,\tau) = \sum_{a} \theta_{a,0}(2z, 4\tau);
• if all is zero and ab is nonzero, \theta_{a,b}(z,\tau) = \exp\bigl(\pi i a^T\tau a/4 + \pi i a^T(z + \tfrac b2)\bigr) \theta_{0,0}(z + \tau\tfrac{a}{2} + \tfrac{b}{2}, \tau), which reduces to the previous case (for derivatives, the exponential factor is expanded with acb_theta_jet_exp_pi_i); with sqr, the value is squared at the end.

@misc{flint-doc-acb-theta-acb-theta-jet-notransform,
  author       = {{The FLINT team}},
  title        = {{acb\_theta\_jet\_notransform (acb\_theta.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/acb_theta/acb_theta_jet_notransform.html},
  note         = {Generated 2026-10-20}
}