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minor doc edits

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This commit is contained in:
Fredrik Johansson 2016-09-14 13:47:33 +02:00
parent be7e0e86fc
commit 2aace2828d
1 changed files with 6 additions and 6 deletions
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12
doc/source/acb_dirichlet.rst
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@ -226,7 +226,7 @@ No discrete log computation is performed.
.. function:: ulong acb_dirichlet_char_order(const acb_dirichlet_char_t chi)
Return the order of `\chi_q(a,\cdot)` which is the order of `a\mod q`.
Return the order of `\chi_q(a,\cdot)` which is the order of `a\bmod q`.
This number is precomputed for the *char* type.
.. function:: acb_dirichlet_char_is_real(const acb_dirichlet_char_t chi)
@ -328,7 +328,7 @@ Gauss and Jacobi sums
.. math::
G_q(a) = \sum_{x \mod q} \chi_q(a, x)e^{\frac{2i\pi x}q}
G_q(a) = \sum_{x \bmod q} \chi_q(a, x)e^{\frac{2i\pi x}q}
.. function:: void acb_dirichlet_jacobi_sum(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi1, const acb_dirichlet_char_t chi2, slong prec)
@ -336,7 +336,7 @@ Gauss and Jacobi sums
.. math::
J_q(a,b) = \sum_{x \mod q} \chi_q(a, x)\chi_q(b, 1-x)
J_q(a,b) = \sum_{x \bmod q} \chi_q(a, x)\chi_q(b, 1-x)
Theta sums
-------------------------------------------------------------------------------
@ -355,16 +355,16 @@ For `\Re(t)>0` we write `x(t)=\exp(-\frac{\pi}{N}t^2)` and define
\Theta_q(a,t) = \sum_{n\geq 0} \chi_q(a, n) x(t)^{n^2}.
.. function:: void acb_dirichlet_chi_theta_arb(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t t, slong prec);
.. function:: void acb_dirichlet_chi_theta_arb(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t t, slong prec)
.. function:: void acb_dirichlet_ui_theta_arb(acb_t res, const acb_dirichlet_group_t G, ulong a, const arb_t t, slong prec);
.. function:: void acb_dirichlet_ui_theta_arb(acb_t res, const acb_dirichlet_group_t G, ulong a, const arb_t t, slong prec)
Compute the theta series `\Theta_q(a,t)` for real argument `t>0`.
Beware that if `t<1` the functional equation
.. math::
t \theta(a,t) = \epsilon(\chi) \theta(\frac1a, \frac1t)
t \theta(a,t) = \epsilon(\chi) \theta\left(\frac1a, \frac1t\right)
should be used, which is not done automatically (to avoid recomputing the
Gauss sum).