arith_ramanujan_tau_series
Synopsis
#include <flint/arith.h>void arith_ramanujan_tau_series(fmpz_poly_t res, slong n)sourceSets res to the polynomial with coefficients \tau(0), \tau(1), \ldots, \tau(n-1), using Jacobi's identity
\Delta(q) = q \Biggl( \sum_{k \ge 0} (-1)^k (2k+1) q^{k(k+1)/2}
\Biggr)^8,
evaluated with three squarings of which the first, of a very sparse series, is done directly.
Cite this page
The FLINT team, “arith_ramanujan_tau_series (arith.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arith/arith_ramanujan_tau_series.html (generated 2026-10-20).
@misc{flint-doc-arith-arith-ramanujan-tau-series,
author = {{The FLINT team}},
title = {{arith\_ramanujan\_tau\_series (arith.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arith/arith_ramanujan_tau_series.html},
note = {Generated 2026-10-20}
}