\\% Multisection of Eta-product and Theta3
\\ Author: Joerg Arndt
\\ License: GPL version 3 or later
\\ online at http://www.jjj.de/pari/
\\ version: 2011-January-19 (12:51)


\r eta.gpi  \\ for chkN_()

\\ Multisection of eta-product:
\\ return series prod( n=1, \infty,  1-x^n )
\\ but only coefficients of x == s (mod m)
Eta_msect(x,s,m,N=-1)=
{
    local(et_, xx);
    chkN_(N);
    \\ eta(x) == 1 + sum(n=1,N,(-1)^n*x^(n*(3*n-1)/2)*(1+x^n))
    et_ = if(s==0, 1, 0);
    for (n=1,N,
        xx = (n*(3*n-1)/2);
        if ( (xx%m)==s, et_ += (-1)^n*x^xx);
        xx = (n*(3*n+1)/2);
        if ( (xx%m)==s, et_ += (-1)^n*x^xx);
    );
    return( et_ );
} /* ----- */

Theta3_msect(x,s,m,N=-1)=
{
    local(th_, xx);
    chkN_(N);
    tt_ = if(s==0, 1, 0);
    for (n=-N,N,
        xx = n^2;
        if ( (xx%m)==s, th_ += x^xx);
    );
    return( th_ );
} /* ----- */




\\ ==== end of file ====