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l_jet: hack to call proper Riemann zeta code

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This commit is contained in:
Fredrik Johansson 2016-12-02 14:41:17 +01:00
parent 253aeba284
commit 6ee1499a5d
2 changed files with 40 additions and 19 deletions
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21
acb_dirichlet/l_jet.c
View file

@ -13,6 +13,10 @@
#include "acb_dirichlet.h" #include "acb_dirichlet.h"
#include "acb_poly.h" #include "acb_poly.h"
/* todo: move implemetation to the acb_dirichlet module */
void _acb_poly_zeta_cpx_reflect(acb_ptr t, const acb_t h,
const acb_t a, int deflate, slong len, slong prec);
void void
acb_dirichlet_l_jet(acb_ptr res, const acb_t s, acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
const dirichlet_group_t G, const dirichlet_char_t chi, const dirichlet_group_t G, const dirichlet_char_t chi,
@ -28,13 +32,20 @@ acb_dirichlet_l_jet(acb_ptr res, const acb_t s,
if (len <= 0) if (len <= 0)
return; return;
/* todo: reflection formula */ /* special-case Riemann zeta */
if (G == NULL || G->q == 1) if (G == NULL || G->q == 1)
{ {
acb_init(a); if (len == 1 && !deflate)
acb_one(a); {
_acb_poly_zeta_cpx_series(res, s, a, deflate, len, prec); acb_dirichlet_zeta(res, s, prec);
acb_clear(a); }
else
{
acb_init(a);
acb_one(a);
_acb_poly_zeta_cpx_reflect(res, s, a, deflate, len, prec);
acb_clear(a);
}
return; return;
} }

38
acb_poly/zeta_series.c
View file

@ -78,29 +78,25 @@ _acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate,
} }
void void
_acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec) _acb_poly_zeta_cpx_reflect(acb_ptr t, const acb_t h, const acb_t a, int deflate, slong len, slong prec)
{ {
slong i;
acb_ptr t, u;
hlen = FLINT_MIN(hlen, len);
t = _acb_vec_init(len);
u = _acb_vec_init(len);
/* use reflection formula */ /* use reflection formula */
if (arf_sgn(arb_midref(acb_realref(h))) < 0 && acb_is_one(a)) if (arf_sgn(arb_midref(acb_realref(h))) < 0 && acb_is_one(a))
{ {
/* zeta(s) = (2*pi)**s * sin(pi*s/2) / pi * gamma(1-s) * zeta(1-s) */ /* zeta(s) = (2*pi)**s * sin(pi*s/2) / pi * gamma(1-s) * zeta(1-s) */
acb_t pi; acb_t pi, hcopy;
acb_ptr f, s1, s2, s3, s4; acb_ptr f, s1, s2, s3, s4, u;
slong i;
acb_init(pi); acb_init(pi);
acb_init(hcopy);
f = _acb_vec_init(2); f = _acb_vec_init(2);
s1 = _acb_vec_init(len); s1 = _acb_vec_init(len);
s2 = _acb_vec_init(len); s2 = _acb_vec_init(len);
s3 = _acb_vec_init(len); s3 = _acb_vec_init(len);
s4 = _acb_vec_init(len); s4 = _acb_vec_init(len);
u = _acb_vec_init(len);
acb_set(hcopy, h);
acb_const_pi(pi, prec); acb_const_pi(pi, prec);
@ -118,13 +114,13 @@ _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int
_acb_vec_scalar_div(s2, s2, len, pi, prec); _acb_vec_scalar_div(s2, s2, len, pi, prec);
/* s3 = gamma(1-s) */ /* s3 = gamma(1-s) */
acb_sub_ui(f, h, 1, prec); acb_sub_ui(f, hcopy, 1, prec);
acb_neg(f, f); acb_neg(f, f);
acb_set_si(f + 1, -1); acb_set_si(f + 1, -1);
_acb_poly_gamma_series(s3, f, 2, len, prec); _acb_poly_gamma_series(s3, f, 2, len, prec);
/* s4 = zeta(1-s) */ /* s4 = zeta(1-s) */
acb_sub_ui(f, h, 1, prec); acb_sub_ui(f, hcopy, 1, prec);
acb_neg(f, f); acb_neg(f, f);
_acb_poly_zeta_cpx_series(s4, f, a, 0, len, prec); _acb_poly_zeta_cpx_series(s4, f, a, 0, len, prec);
for (i = 1; i < len; i += 2) for (i = 1; i < len; i += 2)
@ -137,7 +133,7 @@ _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int
/* add 1/(1-(s+t)) = 1/(1-s) + t/(1-s)^2 + ... */ /* add 1/(1-(s+t)) = 1/(1-s) + t/(1-s)^2 + ... */
if (deflate) if (deflate)
{ {
acb_sub_ui(u, h, 1, prec); acb_sub_ui(u, hcopy, 1, prec);
acb_neg(u, u); acb_neg(u, u);
acb_inv(u, u, prec); acb_inv(u, u, prec);
for (i = 1; i < len; i++) for (i = 1; i < len; i++)
@ -146,16 +142,30 @@ _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int
} }
acb_clear(pi); acb_clear(pi);
acb_clear(hcopy);
_acb_vec_clear(f, 2); _acb_vec_clear(f, 2);
_acb_vec_clear(s1, len); _acb_vec_clear(s1, len);
_acb_vec_clear(s2, len); _acb_vec_clear(s2, len);
_acb_vec_clear(s3, len); _acb_vec_clear(s3, len);
_acb_vec_clear(s4, len); _acb_vec_clear(s4, len);
_acb_vec_clear(u, len);
} }
else else
{ {
_acb_poly_zeta_cpx_series(t, h, a, deflate, len, prec); _acb_poly_zeta_cpx_series(t, h, a, deflate, len, prec);
} }
}
void
_acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec)
{
acb_ptr t, u;
hlen = FLINT_MIN(hlen, len);
t = _acb_vec_init(len);
u = _acb_vec_init(len);
_acb_poly_zeta_cpx_reflect(t, h, a, deflate, len, prec);
/* compose with nonconstant part */ /* compose with nonconstant part */
acb_zero(u); acb_zero(u);