FLINT3.7.0-dev
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arith_ramanujan_tau_series

Synopsis#include <flint/arith.h>
void arith_ramanujan_tau_series(fmpz_poly_t res, slong n)source

Sets res to the polynomial with coefficients τ(0),τ(1),…,τ(n−1)\tau(0), \tau(1), \ldots, \tau(n-1), using Jacobi's identity

Δ(q)=q(∑k≥0(−1)k(2k+1)qk(k+1)/2)8,\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 2026-11-02).