acb_theta_g2_chi3_6
Synopsis
#include <flint/acb_theta.h>void acb_theta_g2_chi3_6(acb_poly_t res, acb_srcptr dth, slong prec)sourceSets res to the vector-valued cusp form \chi_{3,6} of weight \det^3\otimes \mathrm{Sym}^6 with character, given the first derivatives dth of all 16 theta functions at z = 0 (as computed by acb_theta_jet with ord = 1 and all set) [CFG2017]: \chi_{3,6}(\tau) = \frac{1}{64\pi^6} \prod_{(a,b) \text{ odd}} \left(\frac{\partial \theta_{a,b}}{\partial z_1}(0,\tau) x_1 + \frac{\partial\theta_{a,b}}{\partial z_2}(0,\tau) x_2\right).
References#
- [CFG2017] F. Cléry, C. Faber, and G. van der Geer. "Covariants of binary sextics and vector-valued Siegel modular forms of genus two", Math. Ann. 369 (2017), 1649–1669. https://doi.org/10.1007/s00208-016-1510-2
Cite this page
The FLINT team, “acb_theta_g2_chi3_6 (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_chi3_6.html (generated 2026-10-20).
@misc{flint-doc-acb-theta-acb-theta-g2-chi3-6,
author = {{The FLINT team}},
title = {{acb\_theta\_g2\_chi3\_6 (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_chi3_6.html},
note = {Generated 2026-10-20}
}