Class automorphy_system

An instance of this class encapsulates information about automorphic functions for $HX(a_H)$

Field: a_H::RR1

This is the relevant value of a_H. WARNING: various things will work incorrectly if this field is different from the global variable a_H0. This is poor design, but significant effort would be required to fix it.

Field: poly_deg::posint = 100

degree of approximating polynomials

Field: band_number::posint = 3

controls the number of group elements to sum over

Field: p_series::table

A power series approximation to the function $p_{jk}(z)=\sum_{\gamma}\gamma(z)^j\gamma'(z)^k$.

Field: a_star

This is the constant $a^*$, as defined in Section sec-hol-forms

Field: m_series

This is the function $m(z)$, as defined in Section sec-hol-forms

Method: num_group_elements()

This returns the number of group elements that we sum over. It increases rapidly with the band number.

Method: p(j,k,z::CC1)

This calculates individual values of the function $p_{jk}(z)$.

Method: set_p_series(j,k)

This calculates a power series approximation to $p_{jk}(z)$

Method: set_p0_series(k)

This calculates a power series approximation to $p_{0k}(z)$, with some optimizations for this particular case

Method: set_m_series()

This calculates $a^*$ and $m(z)$