FLINT3.7.0-dev
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gr_eisenstein_e, gr_eisenstein_g, gr_eisenstein_g_vec

Synopsis#include <flint/gr_special.h>
int gr_eisenstein_e(gr_ptr res, ulong n, gr_srcptr tau, gr_ctx_t ctx)source
int gr_eisenstein_g(gr_ptr res, ulong n, gr_srcptr tau, gr_ctx_t ctx)source
int gr_eisenstein_g_vec(gr_ptr res, gr_srcptr tau, slong len, gr_ctx_t ctx)source

Set res to the Eisenstein series Gk(τ)=∑(m,n)≠(0,0)(m+nτ)−kG_k(\tau) = \sum_{(m,n) \ne (0,0)} (m + n\tau)^{-k} or its normalisation Ek(τ)=Gk(τ)/(2ζ(k))E_k(\tau) = G_k(\tau) / (2 \zeta(k)), for even k≥2k \ge 2 (GR_DOMAIN for odd kk or k=0k = 0); gr_eisenstein_g_vec writes G4,G6,…,G2len+2G_4, G_6, \ldots, G_{2\mathit{len}+2}.

Cite this page

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