`acb_theta_g2_chi35`

Synopsis#include <flint/acb_theta.h>

void acb_theta_g2_chi35(acb_t res, acb_srcptr th, slong prec)source

Sets res to the cusp form $\chi_{35}$ , the unique scalar Siegel modular form of weight 35 up to scalars, normalised as $\chi_{35}(\tau) = q_1^2 q_3^2 (q_1 - q_3 )(q_2 - q_2^{-1}) + \cdots$ , given the 16 theta constants th, by the formula of Bolza [Bol1887] (see [Mum1984, Prop. 6.2, p. 98] for Bolza's notation in terms of characteristics).

References#

[Bol1887] O. Bolza, "Darstellung der rationalen ganzen Invarianten der Binärform sechsten Grades durch die Nullwerthe der zugehörigen Theta-Functionen", Math. Ann. 30:4 (1887), 478–495. https://doi.org/10.1007/BF01444091
[Mum1984] D. Mumford, Tata Lectures on Theta II, Birkhäuser, 1984. https://doi.org/10.1007/978-0-8176-4578-6

Cite this page

The FLINT team, “acb_theta_g2_chi35 (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/acb_theta_g2_chi35.html (generated 2026-11-02).

@misc{flint-doc-acb-theta-acb-theta-g2-chi35,
  author       = {{The FLINT team}},
  title        = {{acb\_theta\_g2\_chi35 (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_g2_chi35.html},
  note         = {Generated 2026-11-02}
}

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