arb/acb_dirichlet.h

/*=============================================================================

    This file is part of ARB.

    ARB is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    ARB is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with ARB; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2015 Jonathan Bober
    Copyright (C) 2016 Fredrik Johansson

******************************************************************************/

#ifndef ACB_DIRICHLET_H
#define ACB_DIRICHLET_H

#include "acb.h"

#ifdef __cplusplus
extern "C" {
#endif

typedef struct
{
    ulong q;                /* modulus */
    ulong q_even;           /* even part of modulus */
    ulong q_odd;            /* odd part of modulus */
    ulong phi_q;            /* phi(q) */
    ulong phi_q_odd;        /* phi(q_odd) */
    slong num;              /* number of odd prime factors */
    ulong * primes;         /* odd primes p[k] */
    ulong * exponents;      /* exponents e[k] */
    ulong * generators;     /* generator for each odd prime p[k] */
    ulong * PHI;            /* PHI(k) = phi(q_odd) / phi(p[k]^e[k])  */
}
acb_dirichlet_group_struct;

typedef acb_dirichlet_group_struct acb_dirichlet_group_t[1];

void _acb_dirichlet_euler_product_real_ui(arb_t res, ulong s,
    const signed char * chi, int mod, int reciprocal, slong prec);

void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);

void acb_dirichlet_group_init(acb_dirichlet_group_t G, ulong q);

void acb_dirichlet_group_clear(acb_dirichlet_group_t G);

void _acb_dirichlet_group_chi(acb_t res, const acb_dirichlet_group_t G, ulong m, ulong n, slong prec);

#ifdef __cplusplus
}
#endif

#endif