FLINT3.7.0-dev
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_acb_poly_powsum_one_series_sieved

Synopsis#include <flint/acb_poly.h>
void _acb_poly_powsum_one_series_sieved(acb_ptr z, const acb_t s, slong n, slong len, slong prec)source

Sets {z, len} to ∑k=1nk−(s+t)\sum_{k=1}^{n} k^{-(s+t)} as a power series in tt. Powers of composite k=ijk = ij are computed as products i−(s+t)j−(s+t)i^{-(s+t)} j^{-(s+t)} of stored powers, and the even terms are grouped as a polynomial in 2−(s+t)2^{-(s+t)}. This takes about n/log⁡nn / \log n powers, n/2n/2 multiplications and storage for n/6n/6 power series, and is faster than the naive algorithm only when len is small.

Cite this page

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